State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
|
|
- Bernadette Houston
- 7 years ago
- Views:
Transcription
1 State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence. 1. x + 5x + 6 is an example of a prime polynomial. The statement is false. A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial. The polynomial x + 5x + 6 can be written as (x + )(x + 3), so it is not prime. The polynomial x + 5x + 7 is an example of a prime polynomial.. (x + 5)(x 5) is the factorization of a difference of squares. The factored form of the difference of squares is called the product of a sum a difference. So, (x + 5)(x 5) is the factorization of a difference of squares. The statement is true. 3. (x + 5)(x ) is the factored form of x 3x 10. (x 5)(x + ) is the factored form of x 3x 10. So, the statement is false. 4. Expressions with four or more unlike terms can sometimes be factored by grouping. Using the Distributive Property to factor polynomials with four or more terms is called factoring by grouping because terms are put into groups then factored. So, the statement is true. 5. The Zero Product Property states that if ab = 1, then a or b is 1. The statement is false. The Zero Product Property states that for any real numbers a b, if ab = 0, then a = 0, b = 0, or a b are zero. 6. x 1x + 36 is an example of a perfect square trinomial. Perfect square trinomials are trinomials that are the squares of binomials. So, the statement is true. 7. x 16 is an example of a perfect square trinomial. The statement is false. Perfect square trinomials are trinomials that are the squares of binomials. Page 1
2 So, the statement is true. 7. x 16 is an example of a perfect square trinomial. The statement is false. Perfect square trinomials are trinomials that are the squares of binomials. x 16 is the product of a sum a difference. So, x 16 an example of a difference of squares. 8. 4x x + 7 is a polynomial of degree. true 9. The leading coefficient of 1 + 6a + 9a is 1. The stard form of a polynomial has the terms in order from greatest to least degree. In this form, the coefficient of the first term is called the leading coefficient. For this polynomial, the leading coefficient is The FOIL method is used to multiply two trinomials. false; binomials FOIL Method: To multiply two binomials, find the sum of the products of F the First terms, O the Outer terms, I the Inner terms, L the Last terms. Write each polynomial in stard form. 11. x + + 3x The greatest degree is. Therefore, the polynomial can be rewritten as 3x + x x 4 4 The greatest degree is 4. Therefore, the polynomial can be rewritten as x x + x Page
3 Study Guide degree Review - Chapter 8 the polynomial can be rewritten as 3x + x +. The greatest is. Therefore, 1. 1 x 4 4 The greatest degree is 4. Therefore, the polynomial can be rewritten as x x + x The greatest degree is. Therefore, the polynomial can be rewritten as x + 3x x + 6x x + x The greatest degree is 5. Therefore, the polynomial can be rewritten as 3x + x x + 6x. Find each sum or difference (x + ) + ( 3x 5) 16. a + 5a 3 (a 4a + 3) esolutions Cognero 17. (4x Manual 3x +- Powered 5) + (xby 5x + 1) Page 3
4 17. (4x 3x + 5) + (x 5x + 1) 18. PICTURE FRAMES Jean is framing a painting that is a rectangle. What is the perimeter of the frame? The perimeter of the frame is 4x + 4x + 8. Solve each equation. 19. x (x + ) = x(x + x + 1) 0. x(x + 3) = (x + 3) 1. (4w + w ) 6 = w(w 4) + 10 Page 4
5 1. (4w + w ) 6 = w(w 4) GEOMETRY Find the area of the rectangle. 3 The area of the rectangle is 3x + 3x 1x. Find each product. 3. (x 3)(x + 7) 4. (3a )(6a + 5) 5. (3r 7t)(r + 5t) 6. (x + 5)(5x + ) esolutions Manual - Powered by Cognero Page 5
6 6. (x + 5)(5x + ) 7. PARKING LOT The parking lot shown is to be paved. What is the area to be paved? The area to be paved is 10x + 7x 1 units. Find each product. 8. (x + 5)(x 5) 9. (3x ) 30. (5x + 4) 31. (x 3)(x + 3) esolutions Manual - Powered by Cognero Page 6
7 31. (x 3)(x + 3) 3. (r + 5t) 33. (3m )(3m + ) 34. GEOMETRY Write an expression to represent the area of the shaded region. Find the area of the larger rectangle. Find the area of the smaller rectangle. To find the area of the shaded region, subtract the area of the smaller rectangle from the area of the larger rectangle. esolutions by Cognero The Manual area of- Powered the shaded region is 3x 1. Use the Distributive Property to factor each polynomial. Page 7
8 34. GEOMETRY Write an expression to represent the area of the shaded region. Find the area of the larger rectangle. Find the area of the smaller rectangle. To find the area of the shaded region, subtract the area of the smaller rectangle from the area of the larger rectangle. The area of the shaded region is 3x 1. Use the Distributive Property to factor each polynomial x + 4y Factor The greatest common factor of each term is 3 or 1. 1x + 4y = 1(x + y) x y 1xy + 35xy Factor The greatest common factor of each term is 7xy. 14x y 1xy + 35xy = 7xy(x 3 + 5y) 3 esolutions 37. 8xy Manual 16x -ypowered + 10y by Cognero Page 8
9 The greatest of each Study Guide common Review factor - Chapter 8 term is 7xy. 14x y 1xy + 35xy = 7xy(x 3 + 5y) xy 16x y + 10y Factor. The greatest common factor of each term is y xy 16x y + 10y = y(4x 8x + 5) 38. a 4ac + ab 4bc Factor by grouping. 39. x 3xz xy + 3yz 40. 4am 9an + 40bm 15bn Solve each equation. Check your solutions x = 1x Factor the trinomial using the Zero Product Property. or The roots are 0. Check by substituting 0 in for x in the original equation. Page 9
10 Solve each equation. Check your solutions x = 1x Factor the trinomial using the Zero Product Property. or The roots are 0. Check by substituting 0 in for x in the original equation. The solutions are x = 3x Factor the trinomial using the Zero Product Property. The roots are 0 3. Check by substituting 0 3 in for x in the original equation. The solutions are x = 5x Factor the trinomial using the Zero Product Property. Page 10
11 The solutions are x = 5x Factor the trinomial using the Zero Product Property. The roots are 0. Check by substituting 0 in for x in the original equation. The solutions are x(3x 6) = 0 Factor the trinomial using the Zero Product Property. x(3x 6) = 0 x=0 or The roots are 0. Check by substituting 0 in for x in the original equation. The solutions are 0. Page 11
12 Study Guide are Review 8 The solutions 0 - Chapter. 44. x(3x 6) = 0 Factor the trinomial using the Zero Product Property. x(3x 6) = 0 x=0 or The roots are 0. Check by substituting 0 in for x in the original equation. The solutions are GEOMETRY The area of the rectangle shown is x x + 5x square units. What is the length? 3 The area of the rectangle is x x + 5x or x(x x + 5). Area is found by multiplying the length by the width. Because the width is x, the length must be x x + 5. Factor each trinomial. Confirm your answers using a graphing calculator. 46. x 8x + 15 In this trinomial, b = 8 c = 15, so m + p is negative mp is positive. Therefore, m p must both be negative. List the negative factors of 15, look for the pair of factors with a sum of 8. Factors of 15 1, 15 3, 5 Sum of The correct factors are 3 5. Check using a Graphing calculator. Page 1
13 3 The area of thereview rectangle is x x8 + 5x or x(x x + 5). Area is found by multiplying the length by the width. Study Guide - Chapter Because the width is x, the length must be x x + 5. Factor each trinomial. Confirm your answers using a graphing calculator. 46. x 8x + 15 In this trinomial, b = 8 c = 15, so m + p is negative mp is positive. Therefore, m p must both be negative. List the negative factors of 15, look for the pair of factors with a sum of 8. Factors of 15 1, 15 3, 5 Sum of The correct factors are 3 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: x + 9x + 0 In this trinomial, b = 9 c = 0, so m + p is positive mp is positive. Therefore, m p must both be positive. List the positive factors of 0, look for the pair of factors with a sum of 9. Factors of 0 1, 0, 10 4, 5 Sum of The correct factors are 4 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: 1 Page 13
14 Study Guide - Chapter [ 10, 10] scl: Review 1 by [ 10, 10] scl: x + 9x + 0 In this trinomial, b = 9 c = 0, so m + p is positive mp is positive. Therefore, m p must both be positive. List the positive factors of 0, look for the pair of factors with a sum of 9. Factors of 0 1, 0, 10 4, 5 Sum of The correct factors are 4 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: x 5x 6 In this trinomial, b = 5 c = 6, so m + p is negative mp is negative. Therefore, m p must have different signs. List the factors of 6, look for the pair of factors with a sum of 5. Factors of 6 1, 6 1, 6, 3, 3 Sum of The correct factors are 1 6. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 1, 8] scl: 1 Page 14
15 [ 10, 10] scl: 1 by [ 10, 10] scl: x 5x 6 In this trinomial, b = 5 c = 6, so m + p is negative mp is negative. Therefore, m p must have different signs. List the factors of 6, look for the pair of factors with a sum of 5. Factors of 6 1, 6 1, 6, 3, 3 Sum of The correct factors are 1 6. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 1, 8] scl: x + 3x 18 In this trinomial, b = 3 c = 18, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 18, look for the pair of factors with a sum of 3. Factors of 18 1, 18 1, 18, 9, 9 3, 6 3, 6 Sum of The correct factors are 3 6. Check using a Graphing calculator. Page 15
16 [ 10, 10] scl: 1 by [ 1, 8] scl: x + 3x 18 In this trinomial, b = 3 c = 18, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 18, look for the pair of factors with a sum of 3. Factors of 18 1, 18 1, 18, 9, 9 3, 6 3, 6 Sum of The correct factors are 3 6. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 14, 6] scl: 1 Solve each equation. Check your solutions. 50. x + 5x 50 = 0 The roots are Check by substituting 10 5 in for x in the original equation. The solutions are Page 16
17 [ 10, 10] scl: 1 by [ 14, 6] scl: 1 Solve each equation. Check your solutions. 50. x + 5x 50 = 0 The roots are Check by substituting 10 5 in for x in the original equation. The solutions are x 6x + 8 = 0 The roots are 4. Check by substituting 4 in for x in the original equation. The solutions are x + 1x + 3 = 0 Page 17
18 The solutions are x + 1x + 3 = 0 The roots are 8 4. Check by substituting 8 4 in for x in the original equation. The solutions are x x 48 = 0 The roots are 6 8. Check by substituting 6 8 in for x in the original equation. The solutions are x + 11x + 10 = 0 Page 18
19 The solutions are x + 11x + 10 = 0 The roots are Check by substituting 10 1 in for x in the original equation. The solutions are ART An artist is working on a painting that is 3 inches longer than it is wide. The area of the painting is 154 square inches. What is the length of the painting? Let x = the width of the painting. Then, x + 3 = the length of the painting. Because a painting cannot have a negative dimension, the width is 11 inches the length is , or 14 inches. Factor each trinomial, if possible. If the trinomial cannot be factored, write prime x + x 14 In this trinomial, a = 1, b = c = 14, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 1( 14) or 168 identify the factors with a sum of. Factors of 168 Sum, 84 8, , , ,- 4 esolutions Manual Powered by Cognero 38 Page 19 4, , 8
20 Because a painting cannot have a negative dimension, the width is 11 inches the length is , or 14 inches. Factor each trinomial, if possible. If the trinomial cannot be factored, write prime x + x 14 In this trinomial, a = 1, b = c = 14, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 1( 14) or 168 identify the factors with a sum of. Factors of 168 Sum, 84 8, , , , , , 8 The correct factors are 6 8. So, 1x + x 14 = (x 1)(3x + 7). 57. y 9y + 3 In this trinomial, a =, b = 9 c = 3, so m + p is negative mp is positive. Therefore, m p must both be negative. (3) = 6 There are no factors of 6 with a sum of 9. So, this trinomial is prime x 6x 45 In this trinomial, a = 3, b = 6 c = 45, so m + p is negative mp is negative. Therefore, m p must have different signs. List the factors of 3( 45) or 135 identify the factors with a sum of 6. Factors of 135 Sum 1, , , , , 7 5, 7 9, , 15 6 The correct factors are Page 0
21 negative. (3) = 6 There are no factors of 6 with a sum of 9. So, this trinomial is prime x 6x 45 In this trinomial, a = 3, b = 6 c = 45, so m + p is negative mp is negative. Therefore, m p must have different signs. List the factors of 3( 45) or 135 identify the factors with a sum of 6. Factors of 135 Sum 1, , , , , 7 5, 7 9, , 15 6 The correct factors are So, 3x 6x 45 = 3(x 5)(x + 3). 59. a + 13a 4 In this trinomial, a =, b = 13 c = 4, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of ( 4) or 48 identify the factors with a sum of 13. Factors of 48 Sum 1, , 48 47, 4, 4 3, , , 1 8 4, 1 8 6, 8 6, 8 The correct factors are So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator x + x = 4 Page 1
22 So, 3x 6x 45 = 3(x 5)(x + 3). 59. a + 13a 4 In this trinomial, a =, b = 13 c = 4, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of ( 4) or 48 identify the factors with a sum of 13. Factors of 48 Sum 1, , 48 47, 4, 4 3, , , 1 8 4, 1 8 6, 8 6, 8 The correct factors are So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator x + x = 4 The roots are or Confirm the roots using a graphing calculator. Let Y1 = 40x + x Y = 4. Use the intersect option from the CALC menu to find the points of intersection. Page
23 So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator x + x = 4 The roots are or Confirm the roots using a graphing calculator. Let Y1 = 40x + x Y = 4. Use the intersect option from the CALC menu to find the points of intersection. [ 5, 5] scl: 1 by [ 5, 5] scl: 3 The solutions are [ 5, 5] scl: 1 by [ 5, 5] scl: x 3x 0 = 0 The Manual roots are esolutions - Powered or by.5 Cognero 4. Page 3 Confirm the roots using a graphing calculator. Let Y1 = x 3x 0 Y = 0. Use the intersect option from
24 [ 5, 5] scl: 1 by [ 5, 5] scl: 3 [ 5, 5] scl: 1 by [ 5, 5] scl: 3 The solutions. Study Guide are Review - Chapter x 3x 0 = 0 The roots are or.5 4. Confirm the roots using a graphing calculator. Let Y1 = x 3x 0 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. [ 10, 10] scl: 1 by [ 15, 5] scl: 1 The solutions are [ 10, 10] scl: 1 by [ 15, 5] scl: t + 36t 8 = 0 The roots are. Page 4 calculator. Let Y1 = 16t + 36t 8 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. esolutions Manual - Powered by Cognero Confirm the roots using a graphing
25 [ 10, 10] scl: 1 by [ 15, 5] scl: 1 Study Guide are Review - Chapter 8 The solutions 4. [ 10, 10] scl: 1 by [ 15, 5] scl: t + 36t 8 = 0 The roots are. Confirm the roots using a graphing calculator. Let Y1 = 16t + 36t 8 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. [, 3] scl: 1 by [ 0, 10] scl: 6 The solutions are [, 3] scl: 1 by [ 0, 10] scl: x 7x 5 = 0 The roots are or Page 5 Confirm the roots using a graphing calculator. Let Y1 = 6x 7x 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection.
26 [, 3] scl: 1 by [ 0, 10] scl: 6 Study Guide are Review 8 The solutions - Chapter. [, 3] scl: 1 by [ 0, 10] scl: x 7x 5 = 0 The roots are or Confirm the roots using a graphing calculator. Let Y1 = 6x 7x 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. [ 5, 5] scl: 0.5 by [ 10, 10] scl: 1 The solutions are [ 5, 5] scl: 0.5 by [ 10, 10] scl: GEOMETRY The area of the rectangle shown is 6x + 11x 7 square units. What is the width of the rectangle? To find the width, factor the area of the rectangle. In the area trinomial, a = 6, b = 11 c = 7, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 6( 7) or 4 identify the factors with a sum of 11. Factors of 4 Sum 41 1, 4 1, , 1, , 14 3, , 7 6, 7 1 Page 6 The correct factors are 3 14.
27 [ 5, 5] scl: 0.5 by [ 10, 10] scl: 1 [ 5, 5] scl: 0.5 by [ 10, 10] scl: 1 Study Guide are Review - Chapter 8 The solutions. 64. GEOMETRY The area of the rectangle shown is 6x + 11x 7 square units. What is the width of the rectangle? To find the width, factor the area of the rectangle. In the area trinomial, a = 6, b = 11 c = 7, so m + p is positive mp is negative. Therefore, m p must have different signs. List the factors of 6( 7) or 4 identify the factors with a sum of 11. Factors of 4 Sum 41 1, 4 1, , 1, , 14 3, , 7 6, 7 1 The correct factors are So, 6x + 11x 7 = (x 1)(3x + 7). The area of a rectangle is found by multiplying the length by the width. Because the length of the rectangle is x 1, the width must be 3x + 7. Factor each polynomial. 65. y x a 1b The number 1 is not a perfect square. So, 16a 1b is prime. 3 - Powered by Cognero 68. 3x esolutions Manual Page 7
28 67. 16a 1b The number 1 is not a perfect square. So, 16a 1b is prime x 3 Solve each equation by factoring. Confirm your answers using a graphing calculator. 69. a 5 = 0 The roots are 5 5. Confirm the roots using a graphing calculator. Let Y1 = a 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. Thus, the solutions are x 5 = 0 The roots are or about Page 8
29 Study Guide Review Thus, the solutions are - 5Chapter x 5 = 0 The roots are or about Confirm the roots using a graphing calculator. Let Y1 = 9x 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection. Thus, the solutions are y = 0 esolutions - Powered The Manual roots are -9 by9.cognero Page 9 Confirm the roots using a graphing calculator. Let Y1 = 81 - y Y = 0. Use the intersect option from the
30 Study Guide Review Thus, the solutions are - Chapter y = 0 The roots are Confirm the roots using a graphing calculator. Let Y1 = 81 - y Y = 0. Use the intersect option from the CALC menu to find the points of intersection. [-10, 10] scl: 1 by [-10, 90] scl:10 [-10, 10] scl: 1 by [-10, 90] scl:10 Thus, the solutions are x 5 = 0 The roots are Confirm the roots using a graphing calculator. Let Y1 = x - 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection.\ Page 30
31 [-10, 10] scl: 1 by [-10, 90] scl:10 [-10, 10] scl: 1 by [-10, 90] scl:10 Thus, the solutions are x 5 = 0 The roots are Confirm the roots using a graphing calculator. Let Y1 = x - 5 Y = 0. Use the intersect option from the CALC menu to find the points of intersection.\ [-10, 10] scl:1 by [-10, 40] scl: 5 [-10, 10] scl:1 by [-10, 40] scl: 5 Thus, the solutions are EROSION A boulder falls down a mountain into water 64 feet below. The distance d that the boulder falls in t seconds is given by the equation d = 16t. How long does it take the boulder to hit the water? The distance the boulder falls is 64 feet. So, 64 = 16t. The roots are. The time cannot be negative. So, it takes seconds for the boulder to hit the water. Factor each polynomial, if possible. If the polynomial cannot be factored write prime. 74. x + 1x + 36 Page 31
32 [-10, 10] scl:1 by [-10, 40] scl: 5 [-10, 10] scl:1 by [-10, 40] scl: 5 Thus, the solutions are EROSION A boulder falls down a mountain into water 64 feet below. The distance d that the boulder falls in t seconds is given by the equation d = 16t. How long does it take the boulder to hit the water? The distance the boulder falls is 64 feet. So, 64 = 16t. The roots are. The time cannot be negative. So, it takes seconds for the boulder to hit the water. Factor each polynomial, if possible. If the polynomial cannot be factored write prime. 74. x + 1x x + 5x + 5 There are no factors of 5 that have a sum of 5. So, x + 5x + 5 is prime y 1y a + 49a x 1 Page 3
33 4 78. x x 16x Solve each equation. Confirm your answers using a graphing calculator. 80. (x 5) = 11 The roots are Confirm the roots using a graphing calculator. Let Y1 = (x 5) Y = 11. Use the intersect option from the CALC menu to find the points of intersection. [ 0, 0] scl: 3 by [ 5, 15] scl: 13 The Manual solutions are 6by 16. esolutions - Powered Cognero 81. 4c + 4c + 1 = 9 [ 0, 0] scl: 3 by [ 5, 15] scl: 13 Page 33
34 Solve each equation. Confirm your answers using a graphing calculator. 80. (x 5) = 11 The roots are Confirm the roots using a graphing calculator. Let Y1 = (x 5) Y = 11. Use the intersect option from the CALC menu to find the points of intersection. [ 0, 0] scl: 3 by [ 5, 15] scl: 13 [ 0, 0] scl: 3 by [ 5, 15] scl: 13 The solutions are c + 4c + 1 = 9 The roots are 1. Page 34 Confirm the roots using a graphing calculator. Let Y1 = 4c + 4c + 1 Y = 9. Use the intersect option from the CALC menu to find the points of intersection.
35 [ 0, 0] scl: 3 by [ 5, 15] scl: 13 [ 0, 0] scl: 3 by [ 5, 15] scl: 13 Study Guide are Review - Chapter 8 The solutions c + 4c + 1 = 9 The roots are 1. Confirm the roots using a graphing calculator. Let Y1 = 4c + 4c + 1 Y = 9. Use the intersect option from the CALC menu to find the points of intersection. [ 5, 5] scl: 1 by [ 5, 15] scl: [ 5, 5] scl: 1 by [ 5, 15] scl: Thus, the solutions are y = 64 The roots are 4 4. Page 35 Confirm the roots using a graphing calculator. Let Y1 = 4y Y = 64. Use the intersect option from the CALC menu to find the points of intersection.
36 [ 5, 5] scl: 1 by [ 5, 15] scl: Thus, the solutions are 1. [ 5, 5] scl: 1 by [ 5, 15] scl: 8. 4y = 64 The roots are 4 4. Confirm the roots using a graphing calculator. Let Y1 = 4y Y = 64. Use the intersect option from the CALC menu to find the points of intersection. [ 10, 10] scl: 1 by [ 5, 75] scl: 10 [ 10, 10] scl: 1 by [ 5, 75] scl: 10 Thus, the solutions are d + 40d + 5 = 9 The roots are. Page 36
37 [ 10, 10] scl: 1 by [ 5, 75] scl: 10 [ 10, 10] scl: 1 by [ 5, 75] scl: 10 Thus, the solutions are d + 40d + 5 = 9 The roots are. Confirm the roots using a graphing calculator. Let Y1 = 16d + 40d + 5 Y = 9. Use the intersect option from the CALC menu to find the points of intersection. [ 5, 5] scl: 0.5 by [ 5, 15] scl: 5 Thus, the solutions are [ 5, 5] scl: 0.5 by [ 5, 15] scl: LANDSCAPING A sidewalk is being built around a square yard that is 5 feet on each side. The total area of the yard sidewalk is 900 square feet. What is the width of the sidewalk? Let x = width of the sidewalk. Then, x + 5 = the width of the sidewalk yard. Because the yard is square, the width length are the same. Page 37
38 [ 5, 5] scl: 0.5 by [ 5, 15] scl: 5 [ 5, 5] scl: 0.5 by [ 5, 15] scl: 5 Study Guide Review Thus, the solutions are - Chapter LANDSCAPING A sidewalk is being built around a square yard that is 5 feet on each side. The total area of the yard sidewalk is 900 square feet. What is the width of the sidewalk? Let x = width of the sidewalk. Then, x + 5 = the width of the sidewalk yard. Because the yard is square, the width length are the same. The roots are The width of the sidewalk cannot be negative. So, the width of the sidewalk is.5 feet. Page 38
8-8 Differences of Squares. Factor each polynomial. 1. x 9 SOLUTION: 2. 4a 25 SOLUTION: 3. 9m 144 SOLUTION: 4. 2p 162p SOLUTION: 5.
Factor each polynomial. 1.x 9 SOLUTION:.a 5 SOLUTION:.9m 1 SOLUTION:.p 16p SOLUTION: 5.u 81 SOLUTION: Page 1 5.u 81 SOLUTION: 6.d f SOLUTION: 7.0r 5n SOLUTION: 8.56n c SOLUTION: Page 8.56n c SOLUTION:
More information10 7, 8. 2. 6x + 30x + 36 SOLUTION: 8-9 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial.
Squares Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it. 1.5x + 60x + 36 SOLUTION: The first term is a perfect square. 5x = (5x) The last term is a perfect
More information6.3 FACTORING ax 2 bx c WITH a 1
290 (6 14) Chapter 6 Factoring e) What is the approximate maximum revenue? f) Use the accompanying graph to estimate the price at which the revenue is zero. y Revenue (thousands of dollars) 300 200 100
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationFactoring and Applications
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the
More informationOperations with Algebraic Expressions: Multiplication of Polynomials
Operations with Algebraic Expressions: Multiplication of Polynomials The product of a monomial x monomial To multiply a monomial times a monomial, multiply the coefficients and add the on powers with the
More informationTool 1. Greatest Common Factor (GCF)
Chapter 4: Factoring Review Tool 1 Greatest Common Factor (GCF) This is a very important tool. You must try to factor out the GCF first in every problem. Some problems do not have a GCF but many do. When
More informationDefinitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder).
Math 50, Chapter 8 (Page 1 of 20) 8.1 Common Factors Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Find all the factors of a. 44 b. 32
More informationFACTORING OUT COMMON FACTORS
278 (6 2) Chapter 6 Factoring 6.1 FACTORING OUT COMMON FACTORS In this section Prime Factorization of Integers Greatest Common Factor Finding the Greatest Common Factor for Monomials Factoring Out the
More informationFactoring. Factoring Monomials Monomials can often be factored in more than one way.
Factoring Factoring is the reverse of multiplying. When we multiplied monomials or polynomials together, we got a new monomial or a string of monomials that were added (or subtracted) together. For example,
More informationFactor Polynomials Completely
9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping
More informationChapter R.4 Factoring Polynomials
Chapter R.4 Factoring Polynomials Introduction to Factoring To factor an expression means to write the expression as a product of two or more factors. Sample Problem: Factor each expression. a. 15 b. x
More informationGreatest Common Factor (GCF) Factoring
Section 4 4: Greatest Common Factor (GCF) Factoring The last chapter introduced the distributive process. The distributive process takes a product of a monomial and a polynomial and changes the multiplication
More information1.3 Polynomials and Factoring
1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.
More informationFactoring Trinomials: The ac Method
6.7 Factoring Trinomials: The ac Method 6.7 OBJECTIVES 1. Use the ac test to determine whether a trinomial is factorable over the integers 2. Use the results of the ac test to factor a trinomial 3. For
More informationFACTORING ax 2 bx c. Factoring Trinomials with Leading Coefficient 1
5.7 Factoring ax 2 bx c (5-49) 305 5.7 FACTORING ax 2 bx c In this section In Section 5.5 you learned to factor certain special polynomials. In this section you will learn to factor general quadratic polynomials.
More informationFACTORING TRINOMIALS IN THE FORM OF ax 2 + bx + c
Tallahassee Community College 55 FACTORING TRINOMIALS IN THE FORM OF ax 2 + bx + c This kind of trinomial differs from the previous kind we have factored because the coefficient of x is no longer "1".
More informationSPECIAL PRODUCTS AND FACTORS
CHAPTER 442 11 CHAPTER TABLE OF CONTENTS 11-1 Factors and Factoring 11-2 Common Monomial Factors 11-3 The Square of a Monomial 11-4 Multiplying the Sum and the Difference of Two Terms 11-5 Factoring the
More informationHow To Solve Factoring Problems
05-W4801-AM1.qxd 8/19/08 8:45 PM Page 241 Factoring, Solving Equations, and Problem Solving 5 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring
More informationexpression is written horizontally. The Last terms ((2)( 4)) because they are the last terms of the two polynomials. This is called the FOIL method.
A polynomial of degree n (in one variable, with real coefficients) is an expression of the form: a n x n + a n 1 x n 1 + a n 2 x n 2 + + a 2 x 2 + a 1 x + a 0 where a n, a n 1, a n 2, a 2, a 1, a 0 are
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationName Intro to Algebra 2. Unit 1: Polynomials and Factoring
Name Intro to Algebra 2 Unit 1: Polynomials and Factoring Date Page Topic Homework 9/3 2 Polynomial Vocabulary No Homework 9/4 x In Class assignment None 9/5 3 Adding and Subtracting Polynomials Pg. 332
More information6.5 Factoring Special Forms
440 CHAPTER 6. FACTORING 6.5 Factoring Special Forms In this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial. Squaring a binomial.
More informationVeterans Upward Bound Algebra I Concepts - Honors
Veterans Upward Bound Algebra I Concepts - Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER
More informationFactoring a Difference of Two Squares. Factoring a Difference of Two Squares
284 (6 8) Chapter 6 Factoring 87. Tomato soup. The amount of metal S (in square inches) that it takes to make a can for tomato soup is a function of the radius r and height h: S 2 r 2 2 rh a) Rewrite this
More informationNSM100 Introduction to Algebra Chapter 5 Notes Factoring
Section 5.1 Greatest Common Factor (GCF) and Factoring by Grouping Greatest Common Factor for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial. GCF is the
More informationFactoring Flow Chart
Factoring Flow Chart greatest common factor? YES NO factor out GCF leaving GCF(quotient) how many terms? 4+ factor by grouping 2 3 difference of squares? perfect square trinomial? YES YES NO NO a 2 -b
More informationA.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it
Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply
More information6.4 Special Factoring Rules
6.4 Special Factoring Rules OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor a sum of cubes. By reversing the rules for multiplication
More information( ) FACTORING. x In this polynomial the only variable in common to all is x.
FACTORING Factoring is similar to breaking up a number into its multiples. For example, 10=5*. The multiples are 5 and. In a polynomial it is the same way, however, the procedure is somewhat more complicated
More informationMATH 90 CHAPTER 6 Name:.
MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a
More informationFactoring Algebra- Chapter 8B Assignment Sheet
Name: Factoring Algebra- Chapter 8B Assignment Sheet Date Section Learning Targets Assignment Tues 2/17 Find the prime factorization of an integer Find the greatest common factor (GCF) for a set of monomials.
More informationAlum Rock Elementary Union School District Algebra I Study Guide for Benchmark III
Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial
More informationFactoring (pp. 1 of 4)
Factoring (pp. 1 of 4) Algebra Review Try these items from middle school math. A) What numbers are the factors of 4? B) Write down the prime factorization of 7. C) 6 Simplify 48 using the greatest common
More informationBy reversing the rules for multiplication of binomials from Section 4.6, we get rules for factoring polynomials in certain forms.
SECTION 5.4 Special Factoring Techniques 317 5.4 Special Factoring Techniques OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor
More informationFACTORING ax 2 bx c WITH a 1
296 (6 20) Chapter 6 Factoring 6.4 FACTORING a 2 b c WITH a 1 In this section The ac Method Trial and Error Factoring Completely In Section 6.3 we factored trinomials with a leading coefficient of 1. In
More informationCAHSEE on Target UC Davis, School and University Partnerships
UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,
More information5.1 FACTORING OUT COMMON FACTORS
C H A P T E R 5 Factoring he sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. T Today, skydiving is a popular sport around the world.
More informationFactoring Polynomials
Factoring a Polynomial Expression Factoring a polynomial is expressing the polynomial as a product of two or more factors. Simply stated, it is somewhat the reverse process of multiplying. To factor polynomials,
More information15.1 Factoring Polynomials
LESSON 15.1 Factoring Polynomials Use the structure of an expression to identify ways to rewrite it. Also A.SSE.3? ESSENTIAL QUESTION How can you use the greatest common factor to factor polynomials? EXPLORE
More informationSUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills
SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)
More informationMath 10C. Course: Polynomial Products and Factors. Unit of Study: Step 1: Identify the Outcomes to Address. Guiding Questions:
Course: Unit of Study: Math 10C Polynomial Products and Factors Step 1: Identify the Outcomes to Address Guiding Questions: What do I want my students to learn? What can they currently understand and do?
More informationThe majority of college students hold credit cards. According to the Nellie May
CHAPTER 6 Factoring Polynomials 6.1 The Greatest Common Factor and Factoring by Grouping 6. Factoring Trinomials of the Form b c 6.3 Factoring Trinomials of the Form a b c and Perfect Square Trinomials
More informationcalled and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles?
Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first- and second-degree
More informationAlgebra 2 PreAP. Name Period
Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing
More informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.
More informationFactoring Polynomials
Factoring Polynomials Factoring Factoring is the process of writing a polynomial as the product of two or more polynomials. The factors of 6x 2 x 2 are 2x + 1 and 3x 2. In this section, we will be factoring
More informationHow To Factor By Gcf In Algebra 1.5
7-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p
More informationAlgebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test
Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action
More informationPolynomials. Key Terms. quadratic equation parabola conjugates trinomial. polynomial coefficient degree monomial binomial GCF
Polynomials 5 5.1 Addition and Subtraction of Polynomials and Polynomial Functions 5.2 Multiplication of Polynomials 5.3 Division of Polynomials Problem Recognition Exercises Operations on Polynomials
More informationFactoring Guidelines. Greatest Common Factor Two Terms Three Terms Four Terms. 2008 Shirley Radai
Factoring Guidelines Greatest Common Factor Two Terms Three Terms Four Terms 008 Shirley Radai Greatest Common Factor 008 Shirley Radai Factoring by Finding the Greatest Common Factor Always check for
More informationPolynomials and Factoring
7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of
More informationFACTORING POLYNOMIALS
296 (5-40) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated
More informationFactoring Trinomials of the Form x 2 bx c
4.2 Factoring Trinomials of the Form x 2 bx c 4.2 OBJECTIVES 1. Factor a trinomial of the form x 2 bx c 2. Factor a trinomial containing a common factor NOTE The process used to factor here is frequently
More informationWe start with the basic operations on polynomials, that is adding, subtracting, and multiplying.
R. Polnomials In this section we want to review all that we know about polnomials. We start with the basic operations on polnomials, that is adding, subtracting, and multipling. Recall, to add subtract
More informationFactoring Special Polynomials
6.6 Factoring Special Polynomials 6.6 OBJECTIVES 1. Factor the difference of two squares 2. Factor the sum or difference of two cubes In this section, we will look at several special polynomials. These
More information6.1 Add & Subtract Polynomial Expression & Functions
6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic
More informationALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form
ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola
More informationPOLYNOMIALS and FACTORING
POLYNOMIALS and FACTORING Exponents ( days); 1. Evaluate exponential expressions. Use the product rule for exponents, 1. How do you remember the rules for exponents?. How do you decide which rule to use
More information10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED
CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations
More informationQuadratics - Rectangles
9.7 Quadratics - Rectangles Objective: Solve applications of quadratic equations using rectangles. An application of solving quadratic equations comes from the formula for the area of a rectangle. The
More informationMATH 21. College Algebra 1 Lecture Notes
MATH 21 College Algebra 1 Lecture Notes MATH 21 3.6 Factoring Review College Algebra 1 Factoring and Foiling 1. (a + b) 2 = a 2 + 2ab + b 2. 2. (a b) 2 = a 2 2ab + b 2. 3. (a + b)(a b) = a 2 b 2. 4. (a
More informationFACTORING QUADRATICS 8.1.1 through 8.1.4
Chapter 8 FACTORING QUADRATICS 8.. through 8..4 Chapter 8 introduces students to rewriting quadratic epressions and solving quadratic equations. Quadratic functions are any function which can be rewritten
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More information6.6 Factoring Strategy
456 CHAPTER 6. FACTORING 6.6 Factoring Strategy When you are concentrating on factoring problems of a single type, after doing a few you tend to get into a rhythm, and the remainder of the exercises, because
More informationThe Greatest Common Factor; Factoring by Grouping
296 CHAPTER 5 Factoring and Applications 5.1 The Greatest Common Factor; Factoring by Grouping OBJECTIVES 1 Find the greatest common factor of a list of terms. 2 Factor out the greatest common factor.
More informationFactors and Products
CHAPTER 3 Factors and Products What You ll Learn use different strategies to find factors and multiples of whole numbers identify prime factors and write the prime factorization of a number find square
More informationTopic: Special Products and Factors Subtopic: Rules on finding factors of polynomials
Quarter I: Special Products and Factors and Quadratic Equations Topic: Special Products and Factors Subtopic: Rules on finding factors of polynomials Time Frame: 20 days Time Frame: 3 days Content Standard:
More informationFactoring Quadratic Expressions
Factoring the trinomial ax 2 + bx + c when a = 1 A trinomial in the form x 2 + bx + c can be factored to equal (x + m)(x + n) when the product of m x n equals c and the sum of m + n equals b. (Note: the
More informationMTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006
MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order
More informationx 4-1 = (x²)² - (1)² = (x² + 1) (x² - 1) = (x² + 1) (x - 1) (x + 1)
Factoring Polynomials EXAMPLES STEP 1 : Greatest Common Factor GCF Factor out the greatest common factor. 6x³ + 12x²y = 6x² (x + 2y) 5x - 5 = 5 (x - 1) 7x² + 2y² = 1 (7x² + 2y²) 2x (x - 3) - (x - 3) =
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More information5 means to write it as a product something times something instead of a sum something plus something plus something.
Intermediate algebra Class notes Factoring Introduction (section 6.1) Recall we factor 10 as 5. Factoring something means to think of it as a product! Factors versus terms: terms: things we are adding
More information1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)
More information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More informationPre-Calculus II Factoring and Operations on Polynomials
Factoring... 1 Polynomials...1 Addition of Polynomials... 1 Subtraction of Polynomials...1 Multiplication of Polynomials... Multiplying a monomial by a monomial... Multiplying a monomial by a polynomial...
More informationA Systematic Approach to Factoring
A Systematic Approach to Factoring Step 1 Count the number of terms. (Remember****Knowing the number of terms will allow you to eliminate unnecessary tools.) Step 2 Is there a greatest common factor? Tool
More informationUsing the ac Method to Factor
4.6 Using the ac Method to Factor 4.6 OBJECTIVES 1. Use the ac test to determine factorability 2. Use the results of the ac test 3. Completely factor a trinomial In Sections 4.2 and 4.3 we used the trial-and-error
More informationAlgebra Cheat Sheets
Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts
More informationSample Problems. Practice Problems
Lecture Notes Quadratic Word Problems page 1 Sample Problems 1. The sum of two numbers is 31, their di erence is 41. Find these numbers.. The product of two numbers is 640. Their di erence is 1. Find these
More informationFactoring Trinomials using Algebra Tiles Student Activity
Factoring Trinomials using Algebra Tiles Student Activity Materials: Algebra Tiles (student set) Worksheet: Factoring Trinomials using Algebra Tiles Algebra Tiles: Each algebra tile kits should contain
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationThis is Factoring and Solving by Factoring, chapter 6 from the book Beginning Algebra (index.html) (v. 1.0).
This is Factoring and Solving by Factoring, chapter 6 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
More informationCopy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.
Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}
More informationSect 6.1 - Greatest Common Factor and Factoring by Grouping
Sect 6.1 - Greatest Common Factor and Factoring by Grouping Our goal in this chapter is to solve non-linear equations by breaking them down into a series of linear equations that we can solve. To do this,
More informationCHAPTER 7: FACTORING POLYNOMIALS
CHAPTER 7: FACTORING POLYNOMIALS FACTOR (noun) An of two or more quantities which form a product when multiplied together. 1 can be rewritten as 3*, where 3 and are FACTORS of 1. FACTOR (verb) - To factor
More informationMATH 10034 Fundamental Mathematics IV
MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.
More information6.1 The Greatest Common Factor; Factoring by Grouping
386 CHAPTER 6 Factoring and Applications 6.1 The Greatest Common Factor; Factoring by Grouping OBJECTIVES 1 Find the greatest common factor of a list of terms. 2 Factor out the greatest common factor.
More informationFactoring Polynomials
Factoring Polynomials 8A Factoring Methods 8-1 Factors and Greatest Common Factors Lab Model Factoring 8-2 Factoring by GCF Lab Model Factorization of Trinomials 8-3 Factoring x 2 + bx + c 8-4 Factoring
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More informationFactor and Solve Polynomial Equations. In Chapter 4, you learned how to factor the following types of quadratic expressions.
5.4 Factor and Solve Polynomial Equations Before You factored and solved quadratic equations. Now You will factor and solve other polynomial equations. Why? So you can find dimensions of archaeological
More informationPolynomials and Factoring; More on Probability
Polynomials and Factoring; More on Probability Melissa Kramer, (MelissaK) Anne Gloag, (AnneG) Andrew Gloag, (AndrewG) Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required)
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationSOL Warm-Up Graphing Calculator Active
A.2a (a) Using laws of exponents to simplify monomial expressions and ratios of monomial expressions 1. Which expression is equivalent to (5x 2 )(4x 5 )? A 9x 7 B 9x 10 C 20x 7 D 20x 10 2. Which expression
More informationAnswers to Basic Algebra Review
Answers to Basic Algebra Review 1. -1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract
More informationFactoring Polynomials and Solving Quadratic Equations
Factoring Polynomials and Solving Quadratic Equations Math Tutorial Lab Special Topic Factoring Factoring Binomials Remember that a binomial is just a polynomial with two terms. Some examples include 2x+3
More information8-5 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION:
Use the Distributive Property to factor each polynomial. 1. 1b 15a The greatest common factor in each term is 3.. 14c + c The greatest common factor in each term is c. 3. 10g h + 9gh g h The greatest common
More informationAPPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS
APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic
More information