To Factor: Write a polynomial as a product.

Kinds of Factoring:1.GCF2.Difference of Squares3.Trinomials

GCF:- can be done with any number of terms- find what is “common” to both

Factor using GCF:1. 126 x

xx 3010 2

Look For…

(GCF = 6)1. A Number that goes into all terms

2. A variable that is common to all terms

When you have found the GCF, divide each term by the GCF.

=6(x + 2)

2. (GCF = 10x)

=10x(x – 3)

3. 6927 2 xx (GCF = 3)

=3(9x2 + 3x – 2)

Difference of Squares:1. Binomial2. Must be “-”3. Both terms must be perfect squares

1. 2.

3.

94 2 x 81100 2 x

25

9

4

1 2 x

a2 – b2 = (a + b)(a – b)

(2x + 3)(2x – 3)

Use the square roots of the terms!

(10x + 9)(10x – 9)

5

3

2

1

5

3

2

1xx

Factoring TrinomialsTwo Types: in the form x2 + bx + c

OR ax2 + bx + c

For the form x2 + bx + c, …

Review: Multiply (x + 4)(x + 2)

86

8422

2

xx

xxx

Note: The two numbers in thequantities add up to 6 and multiply to 8.

(x + ____)(x + ____)

The two numbers must have a sum of “b” and a product of “c”.

Factor:

1. 2.

3. 4.

1072 xx 1662 xx

24102 xx 34352 xx

(Think of 2 numbers that multiply to 10 and add to 7).

(x + 5)(x + 2)

Multiply to -16 and add to -6.

(x – 8)(x + 2)

(Multiply to -24 and add to 10).

(x + 12)(x – 2)

(Multiply to 34 and add to -35).

(x – 34)( X - 1)

The first coefficient of 2 must be “split” as well as the last constant of 3 must be “split”

so that the “inners” + “outers” = 7

Factoring ax2 + bx + c:

372 2 xx

(____X + ____)(____X + ____)

The blanks with the x must multiply to 2The blanks after the “+” must multiply to 3.When you multiply the inners and outers they must add to 7

(2x + 1)(x + 3)Check with FOIL

Factor:1. 2.

3.

3108 2 xx 7196 2 xx

10596 2 xx

(4x + 1)(2x – 3)

Find factors of 8 and factors of 3

(3x – 1)(2x + 7)

(6x + 1 )(x – 10)