1. Solve x 2 + bx + c = 0 by factoring Section 4.3

2. What is a trinomial????? It has 3 terms connected by addition or subtraction Example : 3x 2 – 6x + 7

4. What are the rules for factoring? TrinomialExampleRules x 2 + bx + cx 2 + 5x + 6All Positive (x + )(x + ) x 2 - bx + cx 2 - 5x + 6b is negative (x - )(x - ) x 2 - bx - cx 2 - 5x - 6c is negative (x - )(x + ) x 2 + bx - cx 2 + 5x - 6c is negative (x - )(x + )

7. How do you decide what numbers go in the parentheses? If the last term is positive: x 2 + 5x + 6 or x 2 - 5x + 6 (x + )(x + ) or (x - )(x - ) (x + 2)(x + 3) or (x – 2)(x – 3) You are looking for 2 numbers that : Multiply = 6 and Add to = 5 2 and 3

8. How do you decide what numbers go in the parentheses? If the last term is negative: x 2 + 5x - 6 or x 2 - 5x - 6 (x - )(x + ) or (x - )(x + ) (x - 1)(x + 6) or (x – 6)(x + 1) You are looking for 2 numbers that : Multiply = 6 and are 5 apart 6 and 1

9. x x Factors of +8: 1 & 8 2 & 4 -1 & -8 -2 & -4 2x + 4x = 6x 1x + 8x = 9x O + I = bx ? -2x - 4x = -6x -1x - 8x = -9x -2 -4

10. Check your answer by using FOIL FOIL

13. Difference of Squares a 2 – b 2 = (a + b)(a – b) x 2 – 9 = (x + 3)(x – 3) 49a 2 – 81 = (7a + 9)(7a – 9)

14. To factor, express each term as a square of a monomial then apply the rule...

15. Here is another example:

17. One your whiteboard D: x 2 + 18x + 32 E: x 2 - 11x + 24 F: x 2 + 10x – 24 G: x 2 - 5x – 36 H: x 2 - 10x + 24

18. Try these on your own: