Factoring a GCF from an Expression

To best understand this lesson, you should make sure you know how to find the GCF of two or more terms. To learn how, see the lesson called Finding a GCF.

3x3 + 27x2 + 9x
To factor out the GCF in an expression like the one above, first find the GCF of all of the expression's terms.

3 (1, 3)
27 (1, 3, 9, 27)
9 (1, 3, 9)

GCF = 3x
Next, write the GCF on the left of a set of parentheses:

3x( )
Next, divide each term from the original expression (3x3+27x2+9x ) by the GCF (3x), then write it in the parenthesis.

3x3 / 3x = x2
27x2 / 3x = 9x
9x / 3x = 3

The next expression we will be factoring is shown below.

36x2 - 64y4
To begin factoring the GCF out of the expression, find the GCF of the two terms.

36 (1, 2, 3, 4, 6, 9, 12, 18, 36)
64 (1, 2, 4, 8, 16, 32, 64)

GCF = 4
As you can see, the two terms to do not have any variables in common, therefore the GCF is simply 4.

Now write 4, the GCF, on the left of a set of parentheses.

4( )
Now divide each term 4, the GCF, and place the result inside the parentheses.

36x2 / 4 = 9x2
-64y4 / 4 = -16y4

4(9x2 - 16y4)
The next page links to various resources and calculators for this lesson.