Factoring Polynomials

FIU has online movies to help with this topic on this page. You must have QuickTime Player, a free download, installed on your computer.

For a slower progression through the techniques of factoring, watch movies 6.9, 6.11-6.15, and 6.17-6.20 on this page.

The University of Idaho provides another online resource. These lectures are only viewable by those with DSL or cable modems. Real Player, a free download, is required to see these videos. The videos cover the topics below. To see the videos, go to this page and look under section R.5.
Factoring a Common Factor
Factoring: Difference of Squares
Factoring: Difference of Cubes
Factoring: Sum of Cubes
Factoring by Grouping
Factoring a trinomial of the form x² + bx + c
Factoring a trinomial of the form ax² + bx + c

More online help:

Factoring out the GCF

Factoring trinomials

Factoring binomials

Factoring polynomials of 4 terms

If you have trouble with the trial-and-error method of factoring trinomials, click here for an alternative approach.

After you have learned all the factoring techniques, we must consider problems that combine two or three of these techniques. We will use the following approach to factoring:

1) Factor out the GCF, if possible

2) If it is a binomial:

look for the difference of squares, difference of cubes, or sum of cubes. See the yellow box on p. 48 of your text.

If it is a trinomial of the form x² + bx + c:

look for 2 numbers that multiply to c and add to b.

If it is a trinomial of the form ax² + bx + c:

use trial-and-error

If it is a polynomial of 4 terms, use the grouping method.

3) Make sure your answer has no factors that can be factored further.

Example: Factor 2y⁴ – 162

Solution: We will follow the three steps outlined above:

1) Factor out the GCF 2:

2(y⁴ – 81)

2) Since we have a binomial, we notice the expression in the parentheses is the difference of two squares

2(y² + 9)(y² – 9)

3) y² – 9 is still the difference of two squares, so it can be factored further

2(y² + 9)(y + 3)(y – 3)