Factoring Using GCF:

To factor using a GCF, take the greatest common factor (GCF), for the numerical coefficient. When choosing the GCF for the variables, if all terms have a common variable, take the ones with the lowest exponent.

Example: 9x⁴ + 3x³ + 12x² GCF: Coefficients = 3

Variables (x) = x²

GCF = 3x²

Next, you just divide each monomial by the GCF!

Answer = 3x²(3x² + x + 4)

Then, check by using the distributive property!

Factoring Trinomials:

Two hints that will help you:

When the last sign is addition, both signs are the same and match the middle term.

When the last sign is subtraction, both signs are different and the larger number goes with the sign of the middle term.

Examples:

Hint #1: Hint #2:

x² – 5x + 6 x² + 5x – 36

(x - )(x - ) (x - )(x + )

Find factors of 6, w/ sum of 5. Find factors of 36 w/ difference of 5.

(x – 3)(x – 2) (x – 4)(x + 9)

CHECK USING FOIL CHECK USING FOIL

Factoring Difference of Two Perfect Squares (DOTS):

When an expression can be viewed as the difference of two perfect squares, for example, a²-b², then we can factor it as (a+b)(a-b).

For example, x² - 25 can be factored as (x+5)(x-5).

This method is based on the pattern (a+b)(a-b)=a² - b², which can be verified by expanding the parentheses in (a+b)(a-b).

Factoring Completely:

When asked to factor completely, you will have to use a combination of the methods that we have used previously.

Factoring completely is a three step process:

1. Factor a GCF from the expression, if possible.

2. Factor a Trinomial, if possible.

3. Factor a Difference Between Two Squares as many times as possible.