Home
#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test
#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator
#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Home » Polynomials » Factoring Polynomials Using the GCF

# Factoring Polynomials

## Lesson 1 - Using the Greatest Common Factor (GCF)

## Factors

## Greatest Common Factor (GCF)

## Example 1

## Example 2

## Example 3

## Other Polynomial Lessons You Might Like

# Like This Page?

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.

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.

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.

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.

- Introduction to Polynomials (Definitions)

- Adding Polynomials

- Subtracting Polynomials

- Multiplying Polynomials

- Using the FOIL Method to Multiply Binomials

- Squaring a Binomial - Using a Special Rule

- Difference of Two Squares - "Special Binomials"

- Factoring Polynomials by Grouping

- Factoring Trinomials

- Factoring Trinomials -Ax
^{2}+Bx+C

Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Custom Search

- FREE Solving Equations E-course
- Algebra Class E-course
- Algebra Class Products
- Algebra Practice Test
- Algebra Readiness Test
- Homework Answer Calculator
- Practice Worksheets

- Site Map
- Pre-algebra Refresher
- Solving Equations
- Graphing Equations
- Writing Equations
- Systems of Equations
- Inequalities
- Functions
- Exponents & Monomials
- Polynomials
- Quadratic Equations
- Algebra 1 Final Exam

- SAT Online Course
- Algebra Cheat Sheets - Very Popular!!
- Algebra Formulas
- Online Resources
- Contact Me
- I Want to Hear From You!
- Algebra Blog
- About Me

Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED

## Comments

We would love to hear what you have to say about this page!