YOU TRY 1 Solve EXAMPLE 2 In-Class Example 2 Solve z2 4z 45 0. Answer: {5, 9} Remember to write down the steps as you are reading the example. Note It is important to remember that the factor p gives us the solution 0. b) At least one of the factors on the left must equal zero for the product to equal zero. (3x 1)(x 7) 0 b R 3x 1 0 x 7 0 Set each factor equal to 0. 3x 1 or x 1 3 x 7 Solve each equation. Check in the original equation: If x 1 3 : If x 7: c 3a 1 3 b 1 d a 1 3 7b 0 3(7) 1(7 7) 0 (1 1) a 22 3 b 0 22(0) 0 ✓ 0 a 22 3 b 0 ✓ The solution set is e 1 3 , 7 f . a) k(k 2) 0 b) (2r 3)(r 6) 0 2 Solve Quadratic Equations by Factoring If the equation is in standard form, ax2 bx c 0, begin by factoring the expression. Solve y2 6y 16 0. Solution y2 6y 16 0 (y 8)(y 2) 0 Factor. b R y 8 0 or y 2 0 Set each factor equal to zero. y 8 or y 2 Solve. Check in the original equation: If y 8: If y 2: (8)2 6(8) 16 0 (2)2 6(2) 16 0 64 48 16 0 ✓ 4 12 16 0 ✓ The solution set is {2, 8}. www.mhhe.com/messersmith SECTION 7.5 Solving Quadratic Equations by Factoring 425
messersmith_power_introductory_algebra_1e_ch4_7_10
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