Factoring PolynomialsLesson 1 - 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. 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. 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
Now, let's take a look at an example that involves more than one variable! Example 2
And... one last example. Example 3
Are you ready to try one on your own? Practice Problem
Answer Key
Polynomials Unit |
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