Greatest Common Factor (GCF)

The first step for factoring a polynomial is to "take out" the greatest common factor.  There are two steps to this:  find the GCF of the numbers and the GCF of the variables.

More info: Basics of factoring & Factoring numbers with afactor tree.

Step 1:  Factor each term completely.  help with this

3•x•x + 3•2•x

Step 2:  Find all factors that are in common (the same in all terms)

3•x•x + 3•2•x

Step 3:  Pull out the GCF and then divide every term by it

Please remember to put parentheses around the terms, with the GCF on the outside. Once you get more advanced, you will probably be able to do the division in your head.

Step 4:  Simplify each term (perform the division)

3x(x + 2)

1)  5x³ - 125x

The GCF is 5x.  Take that out, and then divide each term

5x(x² - 25)     Now factor the binomial in parentheses farther.

2)  4x³ + 6x + 2x²

The GCF is 2x.  Again, take that out.

2x(2x² + 3 + x)

3)  6x²y + 9xy²

The GCF is 3xy.  Notice each term has at least one x and y.

3xy(2x + 3y)

Once you are able to factor thegreatest common factor of a polynomial, you will need to learn other factoring techniques.  Clickhere to find out how to factor trinomials and binomials.

Of course, you can learn the basics of how to factor at ourfactoring main page.  We know that factoring can be an intimidating concept for the beginning algebra student, but don't worry, it only takes a little practice.