9-6: FACTORING TRINOMIALS OF THE TYPE AX2 + BX + CEssential Question: What is the first thing you should look for when factoring a trinomial?

9-6: Factoring ax2 + bx + c

Factoring: The Steps (changes from yesterday in red) Make sure the equation is written in standard form

f(x) = ax2 + bx + c Set up two parenthesis

( )( ) Find two numbers with

A product of a ● c A sum of b

Write answer as (ax ± 1st number)(ax ± 2nd number) Note: This will be wrong (why?) Factor out any GCFs, and remove them

9-6: Factoring ax2 + bx + c

Example #1: c is positive Factor 6n2 + 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)

9-6: Factoring ax2 + bx + c

YOUR TURN Factor each expression 2y2 + 5y + 2

(2y + 1)(y + 2) 6n2 – 23n + 7

(3n – 1)(2n – 7) 2y2 – 5y + 2

(2y – 1)(y – 2)

9-6: Factoring ax2 + bx + c

Example #2: c is negative Factor 7x2 – 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)

9-6: Factoring ax2 + bx + c

YOUR TURN Factor each expression 5d2 – 14d – 3

(5d+1)(d – 3) 2n2 + n – 3

(2n + 3)(n – 1) 20p2 – 31p – 9

(5p – 9)(4p + 1)

9-6: Factoring ax2 + bx + c

Example #3: Keep the GCF Factor 20x2 + 80x + 35

Take out the GCF first. This will be part of the final answer.

5(4x2 + 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)

9-6: Factoring ax2 + bx + c

YOUR TURN Factor each expression 2v2 – 12v + 10

2(v – 1)(v – 5) 4y2 + 14y + 6

2(2y + 1)(y + 3) 18k2 – 12k – 6

6(3k + 1)(k – 1)

9-6: Factoring ax2 + bx + c

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