Definition/Procedure Example Factoring ax2 bx c by trial and error. When approaching a problem in this way, we must keep in mind that we are reversing the FOIL process. (p. 407) Factor by grouping. 5t2 18t 8 5t2 20t 2t 8 5t(t 4) 2(t 4) (t 4)(5t 2) Factor completely. 4x2 16x 15 4x2 15x Write 18t as 20t 2t. 4x2 16x 15 (2x 3)(2x 5) 6x 10x 16x 4x2 16x 15 (2x 3)(2x 5) 7.4 Factoring Special Trinomials and Binomials A perfect square trinomial is a trinomial that results from squaring a binomial. Factoring a Perfect Square Trinomial a2 2ab b2 (a b)2 a2 2ab b2 (a b)2 (p. 413) Factoring the Difference of Two Squares a2 b2 (a b)(a b) (p. 415) 7.5 Solving Quadratic Equations by Factoring A quadratic equation can be written in the form ax2 bx c 0, where a, b, and c are real numbers and a 0. (p. 424) To solve a quadratic equation by factoring, use the zero product rule: If ab 0, then a 0 or b 0. (p. 424) Steps for Solving a Quadratic Equation by Factoring 1) Write the equation in the form ax2 bx c 0. 2) Factor the expression. 3) Set each factor equal to zero, and solve for the variable. 4) Check the answer(s) in the original equation. (p. 426) Factor completely. a) g2 22g 121 (g 11)2 a g b 11 b) 16d 2 8d 1 (4d 1)2 a 4d b 1 Factor completely. w2 64 (w 8)(w 8) (w)2 (8)2 a w, b 8 Some examples of quadratic equations are 5x2 9 0, y2 4y 21, 4( p 2)2 8 7p Solve (y 7)(y 4) 0 b R y 7 0 or y 4 0 Set each factor equal to zero. y 7 or y 4 Solve. The solution set is {7, 4}. Solve 2p2 3p 11 9. 2p2 3p 2 0 Standard form (2p 1)( p 2) 0 Factor. b R 2p 1 0 or p 2 0 2p 1 p 1 2 or p 2 The solution set is e 1 2 , 2 f . Check the answers. 446 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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