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messersmith_power_introductory_algebra_1e_ch4_7_10

Here are the steps to use to solve a quadratic equation by factoring: Procedure Solving a Quadratic Equation by Factoring 1) Write the equation in the form ax2 bx c 0 (standard form) so that all terms are on one side of the equal sign and zero is on the other side. 2) Factor the expression. 3) Set each factor equal to zero, and solve for the variable. (Use the zero product rule.) 4) Check the answer(s) in the original equation. YOU TRY 2 Solve r2 7r 6 0. EXAMPLE 3 In-Class Example 3 Solve each equation by factoring. a) 3d 2 13d 10 b) 4p2 40p c) r 2 8(r 6) d) (a 5)(a 2) 18 Answer: a) e 2 3 , 5 f b) {10, 0} c) {4, 12} d) {1, 8} Solve each equation by factoring. a) 2t2 7t 15 b) 9v2 54v c) h2 5(2h 5) d) (w 4)(w 5) 2 Solution a) Begin by writing 2t2 7t 15 in standard form, at2 bt c 0. 2t2 7t 15 0 Standard form (2t 3)(t 5) 0 Factor. b R 2t 3 0 or  t 5 0 Set each factor equal to zero. 2t 3 t 3 2  or    t 5 Solve. Check in the original equation: If t 3 2 : 2 a3 2 b 2 7a3 2 b 15 2 a9 4 b 21 2 15 9 2 21 2 15 30 2 15 ✓ If t 5: 2(5)2 7(5) 15 2(25) 35 15 50 35 15 ✓ The solution set is e5, 3 2 f . b) Write 9v2 54v in standard form. 9v2 54v 0 Standard form 9v(v 6) 0 Factor. b R 9v 0 or v 6 0 Set each factor equal to zero. v 0 or v 6 Solve. Check. The solution set is {6, 0}. 426 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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