# Factoring Expressions With Exponents

Coming up next: What Is a Scientific Calculator?

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:03 Factoring Expressions…
• 0:42 Example 1
• 2:30 Example 2
• 4:03 Example 3
• 5:31 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Melanie Olczak

Melanie has taught high school Mathematics courses for the past ten years and has a master's degree in Mathematics Education.

This lesson offers a detailed tutorial on how to factor polynomial expressions with exponents. The greatest common factor is used to factor these expressions.

## Factoring Expressions with Exponents

Think of factoring an expression with exponents as dividing that expression by one of its factors. A factor of an expression is a number or expression that divides into the expression evenly. For example, the number 24 has many factors; 1, 2, 3, 4, 6, 8, 12, and 24 are all factors of 24 because they can divide 24 evenly with no remainder.

The greatest common factor, or GCF, of a set of numbers or an expression is the largest number or expression that divides evenly into all of the numbers or terms of the expression.

## Example 1

Let's look at an example to see how this works. We'll take the expression:

To factor, we first must look for the greatest common factor of each term in the expression. There are two things we're going to look at: the coefficient and the exponents of the variables. A coefficient is the number that is multiplied times the variable, or the number in front of the variable. Variables are the letters in the expression. And an exponent is the power of the variable.

In this example, the coefficients are 3 and 12, which have a greatest common factor of 3 since it's the largest number that divides into both numbers evenly.

Second, we look at the variables and, more specifically, the exponents of the variables. In this example, the exponents are 3 and 2. To find the greatest common factor of the variables, we take the lowest exponent, which is 2.

Thus, the greatest common factor of these two terms is:

To factor, we must divide the original expression by the greatest common factor:

To divide, we follow two steps:

• First, we divide the numbers: When we divide 3 by 3, we get 1. When we divide 12 by 3, we get 4.

• Second, we subtract the exponents: When we subtract 2 from 3, we get 1. When we subtract 2 from 2, we get zero. That zero means that there is no longer a variable left. After doing these two steps, we have x minus 4.

Then, to factor, we first write the GCF. In parentheses, we put the quotient that we found when we divided the original expression by the GCF. This means we have:

## Example 2

Let's work through another example. We'll look at:

• First, we find the greatest common factor of the two coefficients. The GCF of 4 and 6 is 2.

• Next, we look at the exponents. The lowest exponent of x is 5, and the lowest exponent of y is 4. So, the GCF of our expression is:

Now, to factor, we divide the original expression by the GCF:

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!

Support