1. 6.4  Factoring Trinomials and

2. Let’s Investigate: Let’s Investigate: (x +4)(x + 3 ) = x 2 +3x +4x +12 = x 2 + 7x +21

3. (x +4)(x + 3) = x 2 +3x +4x +12 = x 2 + 7x +12 Factor: x 2 +7x +12 What set of factors of “12” add up to “7”

4. The Diamond Method product of “a” and “c” “b” Find the two numbers that will multiply to get the top and add to get the bottom.

5. (x +4)(x + 3) = x 2 +3x +4x +12 = x 2 + 7x +12 Factor: x 2 +7x +12 What set of factors of “12” add up to “7” (using the diamond method) 12 7 34

6. Factoring by grouping using the diamond method Use the numbers in the left and right of your diamond as your “x” coefficients to make a 4-term polynomial x 2 + 3x + 4x + 12 Group the first two terms together and the last two terms together (x 2 + 3x) + (4x + 12) Factor out the GCF of each group x(x + 3) + 4(x + 3) Notice that the contents of the parentheses are the same! Use that group as one set of parentheses, and then take the GCF's and put them in a set of parentheses (x + 3)(x + 4) Voila! You've factored the polynomial!

7. Factoring the “bottoms-up” way using the diamond method Set up two sets of parentheses as shown below using the left and right numbers in the diamond (__x + 3)(__x + 4) Divide both of the “numbers” by “a” (__x + 3)(__x + 4) 1 1 “Bottoms-up!” Simplify... (x + 3)(x + 4) Done!

8. Factor using your favorite method:

10. Now...let's try one where the “a” isn't “1” 36 13 94 Let's try it by grouping, first: 6x 2 + 9x + 4x + 6 (6x 2 + 9x) + (4x + 6) 3x(2x + 3) + 2(2x + 3) (2x + 3)(3x + 2) done!

11. Now...the “bottoms-up” method Same equation...6x 2 + 13x + 6 (__ x+ 9)(__x +4) 6 6 Reduce... (__ x+ 3)(__x +2) 2 3 Bottoms-up! (2x + 3)(3x + 2) Done!

12. Factor using your favorite method: 3x 2 + 4x + 1

13. Factor using your favorite method: 8x 2 - 6x - 9

14. A#: Page 276 # 1 – 36 (show the diamond method)