Warm-up Solve each equation. 1. k2 = 81 2. b2 = 169 3. m2 – 196 = 0 4. c2 + 36 = 36 5. 6w2 – 24 = 0 6. 64p2 = 4 k = ±9 b = ±13 m = ±14 c = 0 w = ±2

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

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

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

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

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

Solving a quadratic: 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.

12 3 4 7 Solve by factoring: x2 + 7x + 12 = 0 Factors of 12: 1 and 12

-28 4 -7 -3 Solve by factoring: b2 – 3b – 28 = 0 Factors of -28: 1 and -28 4 -7 2 and -14 -3 4 and -7 (b + 4)(b – 7) = 0 b + 4 = 0 b – 7 = 0 b = -4 b = 7

Solve by factoring: 3a2 + 4a – 4 = 0 Multiply 3 & -4 3a 3a2 6a -12 -2 -2a -4 -1 and 12 11 -2 and 6 4 a 2 -3 and 4 1 (3a – 2)(a + 2) = 0 3a – 2 = 0 a + 2 = 0 +2 +2 -2 -2 3a = 2 a = -2 3 3

Solve by factoring: 3x2 + 16x + 5 = 0 Multiply 3 & 5 x 3x2 1x 15 5 15x 5 1 and 15 16 3 and 5 8 3x 1 (3x + 1)(x + 5) = 0 3x + 1 = 0 x + 5 = 0 -1 -1 -5 -5 3x = -1 x = -5 3 3