header hamburger icon
header search icon

audio read-through Identifying Variable Parts and Coefficients of Terms

Numerical Coefficients and Variable Parts

In a term like 2x, there are two parts that are usually of interest: the numerical part (2) and the variable part (x) .

The numerical part is given a special name it is called the numerical coefficient or, more simply, the coefficient of the term.

In the term 4xy, the coefficient is 4 and the variable part is xy.

In the term 7x2y3, the coefficient is 7 and the variable part is x2y3.

Coefficients 1 and 1

If you don't ‘see’ a coefficient, then it is 1. That is, x=(1)x has coefficient 1. Also, x2y3=(1)x2y3 has coefficient 1. It's never necessary to write a coefficient of 1, because multiplication by 1 doesn't change anything.

In the term x, the coefficient is 1, because x=(1)x. In the term x2y, the coefficient is 1, because x2y=(1)x2y.

Constant Terms

A term like 2 that has no variable part is called a constant term, because it is constant—it never changes. It has no variable part that can ‘hold’ different values. Thus 12, 3, and 9.4 are all constant terms.

Conventional Way to Write Terms

In any term, it is conventional to write the numerical coefficient first. Thus, you should write 4xy, not xy4 or x4y.

Also, it is conventional to write any variable(s) in alphabetical order. Thus, you usually want to write 5xy, not 5yx. Similarly, write x2yz, not yx2z or yzx2.

Note from Dr. Burns (the website creator)
Welcome—so glad you're here!

My sister and I have finished our house-clean-out adventure! This Log House is now for sale via silent bids until July 22, 2025. Here are photos of the house (30 Mt Laurel Way, Monterey, MA). Click on any photo for captions. There is a $700K minimum bid. Contact Carol (email on my homepage) for more information.

Want to say hello? Sign my guestbook!

Example

For this web exercise, when reporting the variable part, variables must be written in alphabetical order. The user input is in bold in the example below.

Consider the term y(3)(2x)(1).

What is the numerical coefficient?  Answer: 6

What is the variable part?  Answer: xy

Write the term in the most conventional way:  Answer: 6xy

Master the ideas from this section by practicing below:

down arrow icon
When you're done practicing, move on to:

Combining Like Terms
right arrow icon

Practice

When reporting the variable part, variables must be written in alphabetical order.

Click ‘New problem’ to begin!
Consider the term:
To get a randomly-generated practice problem, click the ‘New problem’ button above.

Type your answers in the boxes below, pressing ‘Enter’ after each entry.
What is the numerical coefficient?
What is the variable part?
Write the term in the most conventional way:
Want to time yourself? (Algebra Pinball)
Step 2: Click ‘Start timing’ below
    
Desired # problems:
(an even number, please)
Extra work-space?
(units are pixels):