# Factoring Polynomials
Using the Greatest Common Factor (GCF)

There are several methods that can be used when factoring
polynomials. The method that you choose, depends on the make-up of the
polynomial that you are factoring.

In this lesson we will study polynomials that can be factored using the **Greatest Common Factor**.

Make sure that you pay careful attention not only to the process used
for factoring, but also to the make-up of the polynomials that can be
factored using this method.

Let's start by looking at the definition of **factors**.

## Factors

When you factor a polynomial, you are trying to find the quantities
that you multiply together in order to create the polynomial.

Take a look at the following diagram:

Now let's talk about the term **greatest common factor**.

## Greatest Common Factor (GCF)

The **greatest common factor** (GCF) for a polynomial is the largest monomial that is a factor of (divides) each term of the polynomial.

Note: The GCF must be a factor of **EVERY** term in the polynomial.

Take a look at the following diagram:

Before we get started, it may be helpful for you to review the Dividing Monomials lesson. You will need to divide monomials in order to factor polynomials.

Let's take a look at a couple of examples.

## Example 1: Factoring Using the GCF

Not too hard, is it? Look for the GCF and then divide every term by the GCF to see what remains.

Now, let's take a look at an example that involves more than one variable.

## Example 2: Factoring Polynomials

Same process, you just have to be careful to look at all the variables. You must be able to factor out of **every** term in order to identify the GCF.

And... one last example.

## Example 3: Factoring Polynomials

Hopefully you now understand how to factor polynomials if the
polynomials have a greatest common factor. Remember, all polynomial
problems will not have a GCF, and we will discover in the next few
lessons how to factor if there is no GCF.

The next lesson is on factoring by using grouping.

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