1. Factoring Trinomials with ax 2 + bx + c 6x 2 + 11x + 3 1 6 1 3 6 1 3 1 2 3 3 2 Now you need to find the right combination of numbers in the correct order to create the trinomial! Remember to always take out a GCF (if possible) before factoring!

2. 6x 2 + 11x + 3 (x + 1)(6x + 3) does this work? (6x + 1)(x + 3) does this work? (2x + 1)(3x + 3) does this work? (3x + 1)(2x + 3) does this work? YIPPEE!! NOPE YES

3. You can also use “Grouping”! 6x 2 + 11x + 3 2x + 9x Why did I pick 2x and 9x? You cannot just pick any numbers to replace the middle term with … you must follow these directions.

4. Grouping Rules Step 1  multiply a and c Step 2  factor this number Step 3  find the pair that adds to b Step 4  rewrite the problem replacing the middle term with the pair found above Step 5  group, factor out GCF, factor out GCF parenthesis 6x 2 + 11x + 3 (6)(3) = 18 1 18 2 9 3 6 6x 2 + 2x + 9x + 3

5. (6x 2 + 2x) + (9x + 3) Factor out the GCF out of each parenthesis! 2x(3x + 1) + 3(3x + 1) 6x 2 + 2x + 9x + 3  (3x + 1)(2x + 3) Factor out the GCF from the two terms (the parenthesis)

6. What if you grouped different numbers? 6x 2 + 11x + 3 6x + 5x 6x 2 + 6x + 5x + 3 (6x 2 + 6x) + (5x + 3) 6x(x + 1) + 1(5x + 3) That doesn’t work!

7. Another grouping example 6r 2 – r – 12 1) a times c = -72 2) -72 = -9 times 8 3) -9+8=-1! 4)6r 2 – 9r + 8r – 12 5)(6r 2 – 9r) + (8r – 12) 6)3r(2r – 3) +4(2r – 3) 7)(2r – 3)(3r + 4) CHECK IT!!!!!!

8. Factoring Trinomials with ax 2 + bx + c We will call this method/technique the “ac method”, since it starts by multiplying the coefficients a and c to get a trinomial to factor with a = 1.

9. “a c method” * Starting trinomial 6x 2 + 11x + 3 1) Multiply a and c 18 2) Set a = 1 and c to 18 x 2 + 11x + 18 3) Factor the new trinomial (x + 9)(x + 2)

10. 4) Put “a” value back in front of each x (6x + 9)(6x + 2) 5) Take out the GCF from each parenthesis 3(2x + 3) 2(3x + 1) 6) Throw away the GCF and you have your answer (2x + 3)(3x + 1) 7) Check your answer (FOIL) 6x 2 + 11x + 3

11. Another example worked out: 6x 2 + 5x + 1 Step 1  a times c = 6 Step 2  x 2 + 5x + 6 Step 3  (x + 2)(x + 3) Step 4  (6x + 2)(6x + 3) Step 5  2(3x + 1) 3(2x + 1) Step 6  (3x + 1)(2x + 1) Step 7  FOIL to check answer!!! “ac” method

12. Now you try these: 2y 2 + 5y – 12 5m 2 – 9m – 2 4x 2 – 5x + 1 12x 2 – x – 1 6r 2 – r – 12 (y + 4)(2y – 3)

13. ANSWERS!!! 5m 2 – 9m – 2  (5m + 1)(m – 2) 4x 2 – 5x + 1  (4x – 1)(x – 1) 12x 2 – x – 1  (3x – 1)(4x + 1) 6r 2 – r – 12  (2r – 3)(3r + 4) Don’t forget to check your answers