Parts of an Expression: Terms, Factors & Coefficients

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Rewriting Algebraic Expressions Using Structure

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

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:01 Parts of an Expression
  • 1:15 Terms, Factors, and…
  • 3:15 Examples
  • 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

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we will look at some different parts that make up a mathematical expression. Those parts are terms, factors, and coefficients. We will define each of these and see what they look like in various examples.

Parts of an Expression

Do you ever notice that the parts of a whole have their own individual labels and functions, but the whole couldn't function properly without even one of them? For instance, consider a baseball team. When a baseball team is on a field, there are nine different players that take up different positions on the field. There is a pitcher, a catcher, a first, second, and third baseman, a shortstop, and a left, right and center fielder in the outfield.

Each position on the field has its own label and its own function. When we put all these positions together, they work together to make up the whole, and if the team was missing a player at even one of these positions, the team's performance would suffer.

Surprisingly, this concept also applies to mathematical expressions! A mathematical expression is a phrase that contains numbers, variables, symbols and operators grouped together using addition, subtraction, multiplication, and division. For example, 3x 2 + 7x is a mathematical expression. Each mathematical expression has different parts to it, and just like the players on a baseball team, these parts have different labels and different functions. Let's take a look at some of these parts.

Terms, Factors, and Coefficients

As we said, a mathematical expression contains numbers, variables, symbols, and operators connected by addition, subtraction, multiplication, and division. First, let's consider the parts of the expression that are connected with addition and subtraction. These parts are called terms.

Consider our example 3x 2 + 7x. We see that 3x 2 and 7x are connected by addition. Therefore, in this mathematical expression, we call 3x 2 and 7x terms.


partexp2


Next, let's talk about factors in a mathematical expression. In a mathematical expression, factors are parts of the expression that are connected by multiplication. For instance, consider the mathematical expressions 5xy and (x - 2)(x + 5). In the first expression, we see we are multiplying 5 by x by y, so we would call 5, x, and y factors of the mathematical expression. Similarly, in the expression (x - 2)(x + 5), we are multiplying (x - 2) and (x + 5), so we call (x - 2) and (x + 5) factors of the expression.


partexp3


So far, so good, right? Let's consider one more part of a mathematical expression. The coefficients. A coefficient is a number that is multiplied by a variable in a mathematical expression. To illustrate this, consider the terms of our initial example:

3x 2 + 7x. In each of the terms 3x 2 and 7x, x is a variable, and in both terms, we are multiplying a number by the variable. In the first term, 3x 2, 3 is being multiplied by the variable, so 3 is a coefficient. In the second term, 7x, 7 is being multiplied by the variable, so 7 is a coefficient.


partexp4


We see that terms, factors, and coefficients make up mathematical expressions. These parts of an expression each have their own label and function. The more we work with mathematical expressions, the more familiar we will become with these parts, so let's take a look at some examples to really drive this concept home (baseball pun intended).

Examples

Suppose you throw a ball in the air, and the ball's height from the ground can be modeled using the mathematical expression -16x 2 + 20x + 6.


partexp5


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
Support