Coefficients: Definition & Concept

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Leading Coefficient: Definition & Explanation

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

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:00 Coefficients Defined
  • 1:24 Leading Coefficients
  • 2:46 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

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: DaQuita Hester

DaQuita has taught high school mathematics for six years and has a master's degree in secondary mathematics education.

Coefficients come in different forms and can tell you many things about a graph. Learn more about coefficient in this lesson, and check your understanding with a quiz.

Coefficients Defined

Coefficients are the multiplicative numbers located directly in front of a variable, such as x or y. If a number in an equation is not connected with a variable, that number is not considered a coefficient. Instead, it is called a constant. Coefficients can be positive or negative and real or imaginary, as well as decimals, fractions, or whole numbers. Let's take a look at some examples:

  • In the term 5x, the coefficient is the number 5. This coefficient is a whole number that is positive and real.
  • In the term -3y, the coefficient is the number -3. This coefficient is a whole number that is negative and real.
  • For an imaginary coefficient, let's examine the term 2ix. The coefficient for this term is 2i, which is an imaginary whole number.
  • Now, let's look at 3.5z. For this term, 3.5 is our decimal coefficient.

It is important to note that all variables will have a coefficient. If a variable is written without a coefficient, then it is assumed to have a coefficient of 1; frequently, when the coefficient is 1, it is not written. An example of this would be in the equation x + 6. There is no coefficient presented with the variable, so the term x has a coefficient of 1.

Leading Coefficients

A leading coefficient is the coefficient of a term with the highest degree, or largest exponent, within an equation. For example, the degree of the equation 6y^4 + 5y^2 - 2y + 1 is 4, because that is the largest exponent. Therefore, the leading coefficient is 6.

To unlock this lesson you must be a 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

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
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? 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