What is Factoring in Algebra? - Definition & Example

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Find the Prime Factorization of a Number

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

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:03 Parts to a Whole
  • 0:50 Factoring
  • 2:46 Practice
  • 4:57 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed
Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Factoring with ordinary numbers involves knowing that 6 is the product of 2 and 3. But what about factoring in algebra? In this lesson, we'll learn the essential elements of algebra factoring.

Parts to a Whole

Factoring in algebra is a lot like baking. I see you have some cake. Is it your birthday? Oh, I'm sorry - I didn't get you anything. But since I'm here, can I have some?

Mmm, I can really taste the baking soda. Can't you? No? Well there's definitely baking soda in this cake. OK, I can't taste it. That's because it's been combined with other ingredients to form something new - yummy cake.

In algebra, we take expressions and stir them together to make new expressions. But even though it may not be obvious what terms we started with, those ingredients are still there.

You can't take the baking soda out of a finished cake, but you can factor the original terms out of an expression. Let's learn how.


Here is an expression: 4x - 8. Let's say we want to factor it. We can define factoring as finding the terms that are multiplied together to get an expression.

Our expression here has some important parts, like the ingredients we bake with. First, we have two terms: 4x and 8. The terms are the numbers, variables or numbers and variables that are multiplied together. Terms are separated by plus or minus signs.

8 is just a constant, or a number that is what it is. It's constantly 8. x is a variable, or a symbol standing in for a number we don't know. 4 is a coefficient. Notice the prefix 'co-.' The coefficient multiplies a variable. It's a codependent, cooperating coefficient.

Now, we need to find a factor. This is like looking for the baking soda, but usually it's a bit easier. It's more like picking the raisins out of an oatmeal cookie. You may get your hands a little dirty, but your cookie will be less raisin-y for sure.

A factor is a term that can be extracted from the equation. Think about the number 6. Its factors are 2 and 3. Why? Because 2 * 3 is 6.

With 4x - 8, we can extract a 4. Each term is a multiple of 4. If we factor out a 4, we have 4(x - 2). Note that we can reverse what we just did. 4 * x is 4x. And 4 * 2 is 8, getting us back to 4x - 8.

What if we had 3x - 8? Is there a common factor? No. 3 and 8 are what we call relatively prime. Remember that a prime number has no factors other than 1 and itself. Relatively prime numbers have no shared factors other than 1.


Let's practice factoring. Here's an expression: 6y^2 - 11y. OK, what are the factors of 6? 2 and 3. What about 11? 11 is prime. So 6 and 11 are relatively prime. Does that mean we can't factor? Are we going to have to eat the raisins? No! Look at the variables. y^2 and y. We can factor out a y. That gets us y(6y - 11). Cookie crisis averted.

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

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

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.

To learn more, visit our Earning Credit Page

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!
Create an account