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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. 371) 7.3 Special Factoring Techniques 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. 378) Factoring the Difference of Two Squares a2 b2 (a b)(a b) (p. 380) Factoring the Sum and Difference of Two Cubes a3 b3 (a b)(a2 ab b2) a3 b3 (a b)(a2 ab b2) (p. 383) 7.4 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. 392) To solve a quadratic equation by factoring, use the zero product rule: If ab 0, then a 0 or b 0. (p. 393) Factor by grouping. 5n2 18n 8 5n2 20n 2n 8 Write 18n as 20 2n. 5n(n 4) 2(n 4) (n 4)(5n 2) Factor completely. 4x2 16x 15 4x2 15 4x2 16x 15 (2x 3)(2x 5) 6x 10x 16x 4x2 16x 15 (2x 3)(2x 5) Factor completely. a) c2 24c 144 (c 12)2 a c b 12 b) 49p2 56p 16 (7p 4)2 a 7p b 4 Factor completely. d 2 16 (d 4)(d 4) T T (d )2   (4)2 a d,  b 4 Factor completely. w3 27 (w 3)(w)2 (w)(3) (3)2 T T (w)3   (3)3 a w,  b 3 w3 27 (w 3)(w2 3w 9) Some examples of quadratic equations are 3x2 5x 9 0, t2 4t 21, and 2(p 3)2 8 7p. Solve (y 9)(y 4) 0 y 9 0 or y 4 0 Set each factor equal to zero. y 9 or y 4 Solve. The solution set is {9, 4}. www.mhhe.com/messersmith CHAPTER 7 Summary 415


messersmith_power_intermediate_algebra_1e_ch4_7_10
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