Display Title

Definition--Variables, Unknowns, and Constants--Coefficient

What Is a Coefficient?

This is part of a series of definitions that focus on constants, variables, and coefficients. These definition cards can easily be incorporated into a lesson plan.


To see the complete collection of definitions on this topic, click on this link.

The following section provides a brief review of number properties that are helpful in working with numerical and variable expressions.

Brief Review of Factors

When you multiply two numbers, each of them is a factor.


In this example, both 3 and 4 are factors. In fact, you can write any number as the product of its factors.

Three equations showing 12 as the product of its factors.

Brief Review of Algebraic Expressions and Equations

An algebraic expression includes numbers, operations, and variables and is written in the form of a polynomial.

Here is a simple example of an algebraic expression.


Equations can sometimes consist of algebraic expressions, like the one shown below.


Algebraic Expressions with Coefficients

One type of algebraic expression consists of a number multiplied by a variable. Here is an example.

Algebraic expression with 3 as the coefficient

Both the 3 and the x are factors, but with algebraic expressions, the 3 is also called a coefficient. In these algebraic expressions the coefficients are highlighted in red.

Examples of algebraic expressions with coefficients highlighted.

Other Expressions with Coefficients

Here are some other examples of coefficients with exponential, logarithmic, rational, and trigonometric expressions.

Variable expressions with coefficients highlighted.

The downloadable image is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

Note: The download is a PNG file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math definitions on this topic. To see the complete collection of definitions, click on this Link.

To learn more about Slide Show Creator, click on this Link


This resources can also be used with a screen reader. Follow these steps.

  • Click on the Accessibility icon on the upper-right part of the screen.

  • From the menu, click on the Screen Reader button. Then close the Accessibility menu.

  • Click on the PREVIEW button on the left and then click on the definition card. The Screen Reader will read the definition.

Grade Range 6 - 8
Curriculum Nodes Algebra
    • Expressions, Equations, and Inequalities
        • Variables and Unknowns
Copyright Year 2013
Keywords variables, constant, unknowns, definitions, glossary term