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Published byRichard Weaver Modified over 3 years ago

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Warm-up Solve each equation. 1. k 2 = 812. b 2 = m 2 – 196 = 04. c = w 2 – 24 = p 2 = 4 k = ±9b = ±13 m = ±14c = 0 w = ±2

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Section 9.5 Factoring to Solve Quadratic Equations Objective: I will solve quadratic equations by factoring. Standards: 14.0, 23.0, 25.1

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Zero Product Property: If the product of two or more binomials equals 0, then each binomial equals 0. (x + 3)(x + 2) = 0 (x + 3) = 0 and (x + 2) = 0

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(x + 4)(x – 8) = 0 x + 4 = 0 x = (x + 4) = 0 x – 8 = 0 x = 8 +8 (x – 8) = 0 Solve each equation.

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(5x + 4)(2x – 5) = 0 5x + 4 = 0 5x = (5x + 4) = 0 2x – 5 = 0 2x = 5 +5 (2x – 5) = 0 Solve each equation. 5 2

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y(y – 1) = 0 y = 0 y – 1 = 0 y = 1 +1 (y – 1) = 0 Solve each equation.

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If there are three terms: Factor using the X or the box method. Use the zero product property to solve each binomial. Check your answer. Solving a quadratic:

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x 2 + 7x + 12 = Factors of 12: 1 and 12 2 and 6 3 and 4 (x + 3)(x + 4) x + 3 = 0 Solve by factoring: = 0 x = -3 x + 4 = 0 x = -4

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b 2 – 3b – 28 = Factors of -28: 1 and and and -7 (b + 4)(b – 7) b + 4 = 0 Solve by factoring: = 0 b = -4 b – 7 = 0 b = 7

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(3a – 2)(a + 2) = 0 3a 2 6a -4-2a -1 and and a -2 a2 Multiply 3 & and 41 3a 2 + 4a – 4 = 0 Solve by factoring: 3a – 2 = 0a + 2 = a = a = -2

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(3x + 1)(x + 5) = 0 3x 2 1x 515x 1 and 15 3 and x 5 3x1 Multiply 3 & x x + 5 = 0 Solve by factoring: 3x + 1 = 0x + 5 = 0 3x = x = -5

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