From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.


At a Glance - Evaluating Polynomials

Evaluating a polynomial is like evaluating any other expression. We substitute the given value(s) for each and every variable. Then we do the necessary plusing and minusing to find an answer. If you come across a polynomial that involves only subtraction, you may be a little nonplussed.

Sample Problem

Evaluate the polynomial 4x2 – 2x + 7 for x = 3.

We substitute 3 for every occurrence of x to get 4(3)2 – 2(3) + 7 and simplify to 37.

That really wasn't as bad as you were expecting, was it?

Example 1

What is the value of the polynomial 4x2 + 3x + 5 when x = -1?

Example 2

If x = 2 and y = 3, what is the value of the polynomial 4xy + x2xy3?

Exercise 1

What's the value of 5x2 – 3x – 4 when x = -1?

Exercise 2

What's the value of x4 – 16 when x = 2?

Exercise 3

What's the value of 3x3 + 4x2 – 5 when x = -3?

Exercise 4

Evaluate 3xy + 2xy2xy4 for x = 3 and y = -2.

Exercise 5

Evaluate 4x + 3yxy + 2x2y for x = -1 and y = -1.

People who Shmooped this also Shmooped...