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:

Understanding factors in Algebra


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:

How to find the GCF of a polynomial

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

Factoring Using the GCF
Checking your factored solution

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

Factoring Using the GCF

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

Factoring Polynomials
Factoring polynomials continued


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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