1. 9-6: FACTORING TRINOMIALS OF THE TYPE AX 2 + BX + C Essential Question: What is the first thing you should look for when factoring a trinomial?

2. 9-6: Factoring ax 2 + bx + c  Factoring: The Steps (changes from yesterday in red)  Make sure the equation is written in standard form f(x) = ax 2 + bx + c  Set up two parenthesis ( )( )  Find two numbers with A product of a ● c A sum of b  Write answer as (ax ± 1 st number)(ax ± 2 nd number) Note: This will be wrong (why?) Factor out any GCFs, and remove them

3. 9-6: Factoring ax 2 + bx + c  Example #1: c is positive  Factor 6n 2 + 23n + 7 Find the factors of 42 (6 ● 7). Which pair adds to 23? 1 & 42 2 & 21  Winner 3 & 14 6 & 7 (6n + 2)(6n + 21) Factor out GCFs, then cut them out 2(3n + 1) 3(2n + 7) (3n + 1)(2n + 7)

4. 9-6: Factoring ax 2 + bx + c YY OUR T URN FFactor each expression 22y 2 + 5y + 2 (2y + 1)(y + 2) 66n 2 – 23n + 7 (3n – 1)(2n – 7) 22y 2 – 5y + 2 (2y – 1)(y – 2)

5.  Example #2: c is negative  Factor 7x 2 – 26x – 8 Find the factors of -56 (7 ● -8). Which pair adds to -26? 1 & -56 2 & -28  Remember, bigger number is negative here 4 & -14 7 & -8 (7x + 2)(7x – 28) Factor out GCFs, then cut them out (7x + 2) 7(x – 4) (7x + 2)(x – 4)

6. 9-6: Factoring ax 2 + bx + c YY OUR T URN FFactor each expression 55d 2 – 14d – 3 (5d+1)(d – 3) 22n 2 + n – 3 (2n + 3)(n – 1) 220p 2 – 31p – 9 (5p – 9)(4p + 1)

7.  Example #3: Keep the GCF  Factor 20x 2 + 80x + 35 Take out the GCF first. This will be part of the final answer. 5(4x 2 + 16x + 7) Find the factors of 28 (4 ● 7). Which pair adds to 28? 1 & 28 2 & 14  Correct 4 & 7 5(4x + 2)(4x + 14) Factor out GCFs, then cut only these out. The 5 persists. 5 2(2x + 1) 2(2x + 7) 5(2x + 1)(2x + 7)

8. 9-6: Factoring ax 2 + bx + c YY OUR T URN FFactor each expression 22v 2 – 12v + 10 2(v – 1)(v – 5) 44y 2 + 14y + 6 2(2y + 1)(y + 3) 118k 2 – 12k – 6 6(3k + 1)(k – 1)

9.  Assignment  Worksheet #9-6  Problems 1 – 27, all