Extend the concepts of Sections 7.1–7.4 to factor completely. 71) (2z 1)y2 6(2z 1)y 55(2z 1) 72) (2k 7)h2 4(2k 7)h 45(2k 7) 73) (t 3)2 3(t 3) 4 (t 1)(t 4) 74) (v 8)2 14(v 8) 48 v(v 2) 75) (z 7)2 11(z 7) 28 z(z 3) 76) (3n 1)2 (3n 1) 72 (3n 7)(3n 10) (2z 1)(y 11)(y 5) (2k 7)(h 5)(h 9) 77) (a b)2 (a b)2 4ab 78) (x y)2 (x 3y)2 4y(x 2y) 79) (5p 2q)2 (2p q)2 3(7p q)(p q) 80) (4s t)2 (3s 2t)2 (7s t)(s 3t) 81) a2 8a 16 b2 (a b 4)(a b 4) 82) x2 6x 9 y2 (x y 3)(x y 3) 83) s2 18s 81 t2 (s t 9)(s t 9) 84) m2 2m 1 n2 (m n 1)(m n 1) R3) Which critical thinking skills helped you factor polynomials? R1) Some people think of factoring as solving a puzzle. Why do you think they feel that way? R2) Have the procedures and tips you have learned help take most of the “guessing” out of factoring polynomials? 7.5 Solving Quadratic Equations by Factoring What are your objectives for Section 7.5? How can you accomplish each objective? 1 Solve a Quadratic Equation of the Form ab 0 • Learn the defi nition of a quadratic equation and the zero product rule. • Complete the given example on your own. • Complete You Try 1. 2 Solve Quadratic Equations by Factoring • Follow Example 2, and then write the procedure for Solving a Quadratic Equation by Factoring in your own words. • Notice that there is sometimes more than one way to solve a quadratic equation. • Complete the given examples on your own. • Complete You Trys 2 and 3. 3 Solve Higher-Degree Equations by Factoring • A higher-degree equation may already be presented in ab 0 form, but you may need to factor again before solving. • Complete the given example on your own. • Complete You Try 4. www.mhhe.com/messersmith SECTION 7.5 Solving Quadratic Equations by Factoring 423
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