b) At least one of the factors on the left must equal zero for the product to equal zero. (4y 3)(y 9) 0 b R 4y 3 0 or y 9 0 Set each factor equal to 0. 4y 3 y 9 Solve each equation. y 3 4 Check in the original equation: If y 3 4 , If y 9, 4(9) 3 9 9 0 c 4 39(0) 0 ✓ a3 4 b 3 d c 3 4 9 d 0 (3 3) a39 4 b 0 0 a39 4 b 0 ✓ The solution set is e9, 3 4 f . YOU TRY 1 Solve each equation. a) c(c 9) 0 b) (5t 2)(t 7) 0 2 Solve Quadratic Equations by Factoring If the equation is in standard form, ax2 bx c 0, begin by factoring the expression. EXAMPLE 2 Solve m2 6m 40 0. Solution m2 6m 40 0 (m 10)(m 4) 0 Factor. b R m 10 0 or m 4 0 Set each factor equal to zero. m 10 or m 4 Solve. Check in the original equation: If m 10, If m 4, (10)2 6(10) 40 0 (4)2 6(4) 40 0 100 60 40 0 ✓ 16 24 40 0 ✓ The solution set is 54, 106. 394 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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