Use the guess and check strategy and the FOIL method to factor a trinomial.

Transcription

1 A - Factor each polynomial. 5. 7b b 6. 5m n 7mn 0z 0z 6 8s s q 9. 6g gh 0. 6k 5 k 8k. 6y y y. 6 w wz 8w 6z Geometry The area of a rectangle is represented by Its dimensions are represented by binomials in that have prime number coefficients. What are the dimensions of the rectangle? 5. Standardized Test Practice Factor the polynomial wf 8w. A (wf ) w(f ) C w(f 8) D w(f 8) Factoring Trinomials (Pages ) Use the guess and check strategy and the FIL method to factor a trinomial. EXAMPLE Factor 6 First, rewrite the trinomial so that the terms are in descending order. Then check for a GCF ( ) The GCF of the terms is. Use the distributive property. Now factor The product of (?? ) and is. You need to find two integers whose product is and whose sum is. Factors of Sum of Factors, no, no, no, ( ) yes Stop listing factors when you find a pair that works. a y 9yz 8 Answers:., a 0.,, 5, 0 0, y 0 5., 0, y 0, z 0 6., a 0, 5 5 a 0 5 b,, , 5 0., b.,,., a 7, a y,, y 6, 5. D 6 y Glencoe/McGraw-Hill 9 MS Parent and Student Study Guide, Algebra

2 A - [ ( )] ( ) ( ) monomial factor. Select the factors and. Group terms that have a common ( ) ( ) Factor. ( )( ) Use the distributive property. Therefore, 6 8 ( )( ). Complete.. b b 6 (b )(b? ). a a 8 (a? )(a ) 0 (? )( ) k 9k 8 (k 6)(k? ) 5. 8g g (? )(g ) 6. 5n n 8 (5n? )(n ) Factor each trinomial. y 5y 9. k 5k a a. z z. s 9s Geometry The area of a rectangle is (6 7 ) square inches. Find binomial epressions to represent the dimensions of this rectangle. Standardized Test Practice Factor the trinomial v 7v. A (v 7)(v 5) (v )(v ) C (v )(v ) D (v )(v 5) Factoring Differences of Squares (Pages ) You can use the difference of squares rule to factor binomials that can be written in the form a b. Sometimes the terms of a binomial have common factors. If so, the GCF should always be factored out first. Difference of Squares a b (a b)(a b) or (a b)(a b) EXAMPLES A Factor b 9. Factor 7g h 8g 5. b 9 7g h 8g 5 Check for a GCF. (b) (7) b b b and g (h g ) GCF of 7g h and 8g 5 is 7g. (b 7)(b 7) Use the difference of squares. 7g (h g)(h g) h h h and g g g. ab Answers:.. 0ab z 6a 5. b 5n 6. a y c y C 6 9 y Glencoe/McGraw-Hill 9 MS Parent and Student Study Guide, Algebra

3 A - Try These Together Factor each polynomial, if possible. If the polynomial cannot be factored, write prime... y 6 a HINT: oth terms of the binomial must be squares. Also, the sum of two squares cannot be factored using the difference of two squares rule. Factor each polynomial, if possible. If the polynomial cannot be factored, write prime. 9b 5 5. c 7 6. z 6 9z v q 0.9r 0. a b 0.6c. a b c y z. y t 7 t u 5 y 5. 6k 6. Factor y. (Hint: Find fractions that when squared equal and.) 9 6 Standardized Test Practice Factor (y z). A ( y z)( y z) ( y z)( y z) C ( y z)( y z) D ( y z)( y z) Perfect Squares and Factoring (Pages ) Products of the form (a b) and (a b) are called perfect squares, and their epressions are called perfect square trinomials. Perfect Square (a b) a ab b Trinomials (a b) a ab b Factoring a Perfect Square Trinomial You can check whether a trinomial is a perfect square trinomial by checking that the following conditions are satisfied. The first term is a perfect square. The third term is a perfect square. The middle term is either or times the product of the square root of the first term and the square root of the third term. EXAMPLE 0bc 8 b 5 Answers: n 0. 5b. k 5. 8 m a yz a 8 5. n 7n 6. A Glencoe/McGraw-Hill 9 MS Parent and Student Study Guide, Algebra

4 A - Determine whether y y is a perfect square trinomial. If so, factor it. Check each of the following. Is the first term a perfect square? () yes Is the last term a perfect square? y (y) yes Is the middle term twice the product of and y? y ()( y) So, y y is a perfect square trinomial. yes y y () ()(y) (y) ( y) Determine whether each trinomial is a perfect square trinomial. If so, factor it. If the polynomial cannot be factored write prime.. m 6m t t 9 5. y y 6 6. k k Factor each polynomial. If the polynomial cannot be factored write prime. 6 6 q 0q m 0m 5. 00h 9. z 6z 6z 8 n.8n Factor y y 6. (Hint: Check to see if the trinomial is a perfect square trinomial.) Standardized Test Practice Factor the trinomial 5a 0a 5. A (5a ) 5(a ) C (a ) D 5(a ) Solving Equations by Factoring (Pages ) You can use the zero product property to solve equations by factoring. Zero Product Property For all numbers a and b, if ab 0, then a 0, b 0, or both a and b equal 0. EXAMPLES A Solve Rewrite the equation Factor the perfect square trinomial. ( 8)( 8) 0 Answers:.. y a y 7 9. b k 7 k 6 b 6 t n 5 5. y 5y 7 8 t n y 6. D Glencoe/McGraw-Hill 9 MS Parent and Student Study Guide, Algebra

5 A or The solution set is {8}. J E CT I VE 8b S Solve y y 5y y y 5y 0 Rewrite the equation. y(y y 5) 0 Factor the GCF, y. y(y )(y 5) 0 y 0 or y 0 or y 5 0 y y 5 y 5 The solution set is, 0,. y 5 b 0b HINT: Remember that you may have more than one solution, so record your solutions as a solution set. Try These Together Solve each equation. Check each solution.. a 9a Solve each equation. Check each solution. y 7y 5. (z 0)(z 0) 0 6. (a 5)(a 7) 0 z z 0 k 9k g 6 g Geometry The triangle at the right has an area of 6 square inches. Find the height h of the triangle. (Hint: Area of triangle bh) h in. (h ) in. Standardized Test Practice Solve the equation k(k 5)(k 8) 0. A { 5, 8} { 5, 0, 8} C {0, 8, 5} D { 8, 0, 5} Chapter 0 Review Rewind / Fast Forward Rewind by factoring each polynomial completely. Then cross off the answer in the right column. Fast forward by multiplying your answer to check it. The letters that are left will spell an outdated technology. 5y n 6 Answers: d k n a 6 5. k m Glencoe/McGraw-Hill 95 MS Parent and Student Study Guide, Algebra

6 A -6 Rewind. 8 9y y y 6 8. y y. 8y y Fast Forward ( )( y ) E ( )( ) N ( )( ) D ( )( ) W ( )( ) I ( )( ) N ( 8)( 8) G ( 8)( 8) S ( )( ) P ( )( y ) H ( )( y) A a Answers: y a D Glencoe/McGraw-Hill 96 MS Parent and Student Study Guide, Algebra

7 A -7 ( y)( ) T ( )( y ) I ( )( y) ( ) T ( )( ) S ( 8)( 8) R ( 6) A ( ) (6 y) C 9( y) E 9( y) K Graphing Quadratic Functions (Pages 6 67) Quadratic Function Ais of Symmetry A quadratic function is a function that can be written in the form f() a b c where a 0. The graph of a quadratic function is a parabola. a is positive: parabola opens upward and verte is a minimum point of the function a is negative: parabola opens downward and verte is a maimum point of the function Parabolas have symmetry, which means that when they are folded in half on a line that passes through the verte, each half matches the other eactly. This line is called the ais of symmetry. Ais of symmetry for graph of y a b b c, where a 0, is a. EXAMPLE Given the equation y, find the equation for the ais of symmetry, the coordinates of the verte, and graph the equation. In the equation y, a and b. Substitute these values into the equation for the ais of symmetry. b ais of symmetry: a () or Since you know the line of symmetry, you know the -coordinate for the verte is. y y or Replace with. Coordinates of verte: (, y) (, ) Graph the verte and the line of symmetry,. Answers:. 6 8n b m t t 9. 7 n 5 y m 7 t Glencoe/McGraw-Hill 97 MS Parent and Student Study Guide, Algebra

8 A -8 Using the equation, you can find another point on the graph. The point (, 6) is units right of the ais of symmetry. Since the graph is symmetrical, if you go units left of the ais and 6 units up, you will find a third point on the graph, (, 6). Repeat this for several other points. Then sketch the parabola. y (, 6) (, 6) minimum point (, ) = Write the equation of the ais of symmetry and find the coordinates of the verte of the graph of each equation. State if the verte is a maimum or minimum. Then graph the equation.. y 0. y 6 7 y y 8 5. y 6 6. y 8 y y 9. y 0. Standardized Test Practice What is the verte of the graph of y? A (, ) (, 7) C (, ) D (, 7) Solving Quadratic Equations by Graphing (Pages 60 67) The solutions of a quadratic equation are called the roots of the equation. You can find the real number roots by finding the -intercepts or zeros of the related quadratic function. Quadratic equations can have two distinct real roots, one distinct root, or no real roots. These roots can be found by graphing the equation to see where the parabola crosses the -ais. EXAMPLES Describe the real roots of the quadratic equations whose related functions are graphed below. Answers:.., 5, 5. 7, 6. 0, 9. no solution 0. 7,.,., no solution 5. 0, Glencoe/McGraw-Hill 98 MS Parent and Student Study Guide, Algebra

9 A y y C y The parabola crosses the Since the verte of the Connect the -ais twice. ne root is parabola lies on the -ais This parabola does not intersect between and, and the the function has one the -ais, so answers there are no to real each other is between and 5. distinct root,. roots. The solution problem set is in. the following order: Connect # to #. State the real roots of each quadratic equation whose related function is Connect # to # graphed below. Connect #5 to #6. Connect # to # Connect #5 to # 8 Connect #7 to # 5 Connect # to # y y y 6 Answers are located on page Glencoe/McGraw-Hill 99 MS Parent and Student Study Guide, Algebra