When+a+≠+1

Factoring:Whan a ≠ 1 = =

Take out any GCF's in da house. Example 1: 24x^2 + 22x - 10 The GCF here is 2  So...  24x^2 + 22x - 10  BECOMES...  2(12x^2 + 11x - 5)  Now in we take the first and last terms in the trinomial and multiply them together.

12 * -5 = -60

We need a set of numbers that add up to be 11, and whose products are -60.

-1 + 60 = 59 1 + -60 = -59  2 + -30 = -28  -2 + 30 = 28  3 + -20 = -17  -3 + 20 = 17  -4 + 15 = 11 4 + -15 = -11  5 + -12 = -7  -5 + 12 = 7-6 + 10 = 4   6 + -10 = -4

The set that works is -4, 15

Now we substitute them in for 11x

2(12x^2 - 4x + 15x -5)

Now to get the two quantaties we are going to group the new equation like so.

(first two terms) + (second two terms)

(12x^2 - 4x) + (15x - 5)

Now we need to find the GCF's for each quantity.

4x is the GCF for the first.5 is the GCf for the second.We bring those GCF's to the front of the quantities they came out of.

4x(3x - 1) + 5(3x - 1)

The terms left in the parenthesies should match.Now put the numbers in front in their own quantity.

(3x - 1) (4x + 5)

DON'T FOR GET THE TWO FROM BEFORE!Fianl answer:

2(3x - 1) (4x + 5)

Example 2: 2x^2 - x - 3

There is not a GCF in this one.

Multiply the first and last terms.

2 * -3 = -6

Now we need to find a set of number whos product is -6 and add up to -1.

1 + -6 = -5 -1 + 6 = 5 -2 + 3 = 1 __2 + -3 = -1__ Now group and take out the GCF's.

2x^2 + 2x - 3x -3 (2x^2 + 2x) + (- 3x -3)

2x(x + 1) + -3(x +1)

(2x- 3) (x + 1)