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
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 9. 10. 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 +. 1. 1 x 4 4 The greatest degree is 4. Therefore, the polynomial can be rewritten as x + 1. 13. + 3x + x Page
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 + 1. 13. + 3x + x The greatest degree is. Therefore, the polynomial can be rewritten as x + 3x +. 5 14. 3x + 6x x + x 3 5 3 The greatest degree is 5. Therefore, the polynomial can be rewritten as 3x + x x + 6x. Find each sum or difference. 3 3 15. (x + ) + ( 3x 5) 16. a + 5a 3 (a 4a + 3) esolutions Cognero 17. (4x Manual 3x +- Powered 5) + (xby 5x + 1) Page 3
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
1. (4w + w ) 6 = w(w 4) + 10. 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. (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
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
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. 35. 1x + 4y Factor The greatest common factor of each term is 3 or 1. 1x + 4y = 1(x + y) 36. 14x 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
The greatest of each Study Guide common Review factor - Chapter 8 term is 7xy. 14x y 1xy + 35xy = 7xy(x 3 + 5y) 3 37. 8xy 16x y + 10y Factor. The greatest common factor of each term is y. 3 3 8xy 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. 41. 6x = 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
Solve each equation. Check your solutions. 41. 6x = 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 0. 4. 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 0 3. 43. 3x = 5x Factor the trinomial using the Zero Product Property. Page 10
The solutions are 0 3. 43. 3x = 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 0. 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 0. Page 11
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 0. 3 45. 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 8 16 8 The correct factors are 3 5. Check using a Graphing calculator. Page 1
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 8 16 8 The correct factors are 3 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: 1 47. 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 9 1 1 9 The correct factors are 4 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: 1 Page 13
Study Guide - Chapter [ 10, 10] scl: Review 1 by [ 10, 10] scl: 18 47. 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 9 1 1 9 The correct factors are 4 5. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 10, 10] scl: 1 48. 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 5 5 5 1 1 The correct factors are 1 6. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 1, 8] scl: 1 Page 14
[ 10, 10] scl: 1 by [ 10, 10] scl: 1 48. 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 5 5 5 1 1 The correct factors are 1 6. Check using a Graphing calculator. [ 10, 10] scl: 1 by [ 1, 8] scl: 1 49. 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 3 17 17 7 7 3 3 The correct factors are 3 6. Check using a Graphing calculator. Page 15
[ 10, 10] scl: 1 by [ 1, 8] scl: 1 49. 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 3 17 17 7 7 3 3 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 10 5. Check by substituting 10 5 in for x in the original equation. The solutions are 10 5. Page 16
[ 10, 10] scl: 1 by [ 14, 6] scl: 1 Solve each equation. Check your solutions. 50. x + 5x 50 = 0 The roots are 10 5. Check by substituting 10 5 in for x in the original equation. The solutions are 10 5. 51. x 6x + 8 = 0 The roots are 4. Check by substituting 4 in for x in the original equation. The solutions are 4. 5. x + 1x + 3 = 0 Page 17
The solutions are 4. 5. x + 1x + 3 = 0 The roots are 8 4. Check by substituting 8 4 in for x in the original equation. The solutions are 8 4. 53. x x 48 = 0 The roots are 6 8. Check by substituting 6 8 in for x in the original equation. The solutions are 6 8. 54. x + 11x + 10 = 0 Page 18
The solutions are 6 8. 54. x + 11x + 10 = 0 The roots are 10 1. Check by substituting 10 1 in for x in the original equation. The solutions are 10 1. 55. 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 11 + 3, or 14 inches. Factor each trinomial, if possible. If the trinomial cannot be factored, write prime. 56. 1x + 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, 84 8 3, 56 53 3, 56 53 4,- 4 esolutions Manual Powered by Cognero 38 Page 19 4, 4 38 6, 8
Because a painting cannot have a negative dimension, the width is 11 inches the length is 11 + 3, or 14 inches. Factor each trinomial, if possible. If the trinomial cannot be factored, write prime. 56. 1x + 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, 84 8 3, 56 53 3, 56 53 4, 4 38 4, 4 38 6, 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. 58. 3x 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, 135 134 1, 135 134 3, 45 4 3, 45 4 5, 7 5, 7 9, 15 6 9, 15 6 The correct factors are 15 9. Page 0
negative. (3) = 6 There are no factors of 6 with a sum of 9. So, this trinomial is prime. 58. 3x 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, 135 134 1, 135 134 3, 45 4 3, 45 4 5, 7 5, 7 9, 15 6 9, 15 6 The correct factors are 15 9. 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 1, 48 47, 4, 4 3, 16 13 3, 16 13 4, 1 8 4, 1 8 6, 8 6, 8 The correct factors are 3 16. So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator. 60. 40x + x = 4 Page 1
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 1, 48 47, 4, 4 3, 16 13 3, 16 13 4, 1 8 4, 1 8 6, 8 6, 8 The correct factors are 3 16. So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator. 60. 40x + x = 4 The roots are or 0.80 0.75. 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
So, a + 13a 4 = (a 3)(a + 8). Solve each equation. Confirm your answers using a graphing calculator. 60. 40x + x = 4 The roots are or 0.80 0.75. 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: 3. 61. 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
[ 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 8 61. 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: 1 4. 6. 16t + 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
[ 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: 1 6. 16t + 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: 6. 63. 6x 7x 5 = 0 The roots are or 0.5 1.67. 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.
[, 3] scl: 1 by [ 0, 10] scl: 6 Study Guide are Review 8 The solutions - Chapter. [, 3] scl: 1 by [ 0, 10] scl: 6 63. 6x 7x 5 = 0 The roots are or 0.5 1.67. 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: 1. 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, 4 41 19, 1, 1 19 11 3, 14 3, 14 11 1 6, 7 6, 7 1 Page 6 The correct factors are 3 14.
[ 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, 4 41 19, 1, 1 19 11 3, 14 3, 14 11 1 6, 7 6, 7 1 The correct factors are 3 14. 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 81 66. 64 5x 67. 16a 1b The number 1 is not a perfect square. So, 16a 1b is prime. 3 - Powered by Cognero 68. 3x esolutions Manual Page 7
67. 16a 1b The number 1 is not a perfect square. So, 16a 1b is prime. 68. 3x 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 5 5. 70. 9x 5 = 0 The roots are or about -1.667 1.667. Page 8
Study Guide Review Thus, the solutions are - 5Chapter 5. 8 70. 9x 5 = 0 The roots are or about -1.667 1.667. 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. 71. 81 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
Study Guide Review Thus, the solutions are - Chapter 8. 71. 81 y = 0 The roots are -9 9. 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 9 9. 7. x 5 = 0 The roots are -5 5. 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
[-10, 10] scl: 1 by [-10, 90] scl:10 [-10, 10] scl: 1 by [-10, 90] scl:10 Thus, the solutions are 9 9. 7. x 5 = 0 The roots are -5 5. 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 5 5. 73. 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
[-10, 10] scl:1 by [-10, 40] scl: 5 [-10, 10] scl:1 by [-10, 40] scl: 5 Thus, the solutions are 5 5. 73. 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 75. x + 5x + 5 There are no factors of 5 that have a sum of 5. So, x + 5x + 5 is prime. 76. 9y 1y + 4 77. 4 8a + 49a 4 78. x 1 Page 3
4 78. x 1 4 79. x 16x Solve each equation. Confirm your answers using a graphing calculator. 80. (x 5) = 11 The roots are 6 16. 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
Solve each equation. Confirm your answers using a graphing calculator. 80. (x 5) = 11 The roots are 6 16. 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 6 16. 81. 4c + 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.
[ 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 16. 6 81. 4c + 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 1. 8. 4y = 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.
[ 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 4 4. 83. 16d + 40d + 5 = 9 The roots are. Page 36
[ 10, 10] scl: 1 by [ 5, 75] scl: 10 [ 10, 10] scl: 1 by [ 5, 75] scl: 10 Thus, the solutions are 4 4. 83. 16d + 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: 5. 84. 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
[ 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.8 84. 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 7.5.5. The width of the sidewalk cannot be negative. So, the width of the sidewalk is.5 feet. Page 38