1. Solving Quadratic Equations by Factoring

2. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x² + 7x + 12 (x − 1)(x − 2) (x + 3)(x + 4) x = 1 or 2. x = −3 or − 4 c) x² + 3x − 10 d) x² − x − 30 (x + 5)(x − 2) (x + 5)(x − 6) x = −5 or 2 x = −5 or 6.

3. Now let’s solve these quadratics.

4. e) 2x² + 7x + 3 f) 3x² + x − 2 (2x + 1)(x + 3) (3x − 2)(x + 1) x = -1/2 or −3 x = 2 or −1. 3 g) x² + 12x + 36 h) x² − 2x + 1 (x + 6)² ( x − 1)² x = −6, −6 x = 1, 1 A double root A double root.

5. a) x² = 5x − 6 b) x² + 12 = 8x x² − 5x + 6 = 0 x² − 8x + 12 = 0 (x − 2)(x − 3) = 0 (x − 2)(x − 6) = 0 x = 2 or 3. x = 2 or 6. c) 3x² + x = 10 d) 2x² = x 3x² + x − 10 = 0 2x² − x = 0 (3x − 5)(x + 2) = 0 x(2x − 1) = 0 x = 5/3 or − 2. x = 0 or 1/2.

6. Problem 6. Solve for x. a) 3 − 11x− 5x² = 0 2 5x² + 11x -3 = 0 2 10x² + 11x − 6 = 0 (5x − 2 )(2x + 3) = 0 The roots are 2 and −3 5 b) 4 + 11x − 5x² = 0 3 5x² − 11x − 4 = 0 3 15x² − 11x − 12 = 0 (3x − 4)(5x + 3 ) = 0 The roots are 4 and -3. 3 5