1. Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x 2 + 11x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x 2 + 10x + 25 = 0x = -5 5. 6x 2 + x = 15x = 3 / 2 and - 5 / 3

2. 2x 2 – 5x – 12 We know how to factor: - A General Trinomial Solving Polynomial Equations (2x + 3)(x – 4) - A Perfect Square Trinomial x 2 + 10x + 25 (x + 5)(x + 5) = (x +5) 2 - The Difference of two Squares x 2 – 9 (x) 2 – 3 2 (x + 3)(x – 3) - A Common Monomial Factor 6x 2 + 15x 3x(2x + 5)

3. a) x 4 – 6x 2 – 27 Example 1 Factor (x 2 + ?)(x 2 – ?) (x 2 + 3)(x 2 – 9) (x 2 + 3)(x – 3)(x + 3) b) x 4 – 3x 2 – 10 (x 2 + ?)(x 2 – ?) (x 2 + 2)(x 2 – 5)

4. a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Sum of Two Cubes ** Special Factoring Patterns ex. x 3 + 8 a = x (x + 2)(x 2 – 2x + 4) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Example 2 x 3 + 125 x 3 + 5 3 Difference of Two Cubes b = 2 ex. 8x 3 – 1 x 3 + 2 3 a = 2x (2x – 1)(4x 2 + 2x + 1) b = 1 (2x) 3 – (1) 3 = (x + 5)(x 2 – 5x + 25)

5. a) x 3 – 27 Example 3 Factor a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) x 3 – 3 3 = (x – 3)(x 2 + 3x + 9) b) 8x 3 + 64 a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) (2x) 3 + (4) 3 = (2x + 4)(4x 2 – 8x + 16)

6. Must be the same x 2 (x – 2) x 3 – 2x 2 – 9x + 18 (x 2 – 9)(x – 2) Extra Example 2 Factor by grouping -9(x – 2) (x – 3)(x + 3)(x – 2)

7. Solving Polynomial Equations 1.Factor out GCF 2.Factor remaining quadratic equation 1.If remaining equation can not be factored, use quadratic formula. 3.Solve all equations for variable. #1:

8. #3:#7:

9. #6:

10. #1B: What do we do when we can’t factor? Roots:

11. #4B: What do we do when we can’t factor? Roots:

12. #1M : What do we do when we can’t factor? Roots:

13. Homework Handout