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12.4: Evaluate Polynomial Expressions

Difficulty Level: Basic Created by: CK-12
Practice Polynomial Expression Evaluation
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Have you ever thought about a cube? Take a look at this dilemma.

Mr. Travis is taking his Social Studies class on a tour of downtown. He has created a scavenger hunt for the students as they travel around the city. The scavenger hunt is made up of all different types of architecture and landmarks as well as problems that will need to be solved. Mr. Travis asked the bus to drop the students off in front of the town hall. In the square across from the town hall is a plaza with three cubes in it.

“Hey there is a problem with these cubes,” Tanya said to her friend Michael.

Here is the problem on the sheet.

Before you is a cube. Use the formula A = 6s^2 to find the surface area of a cube whose side measures 8 feet.

Tanya looked at Michael who looked at her. Both students began working on the problem in their notebooks.

You can work on this problem too. You will learn about polynomials in this Concept. By the end of the it, you will be able to solve this problem.


A polynomial is an algebraic expression that shows the sum of monomials .

Since the prefix mono means one, a monomial is a single piece or term . The prefix poly means many. So the word polynomial refers to one or more than one term in an expression. The relationship between these terms may be sums or difference.

Polynomials : x^2+ 5 \qquad 3x-8+4x^5 \qquad -7a^2+9b-4b^3+6

We call an expression with a single term a monomial , an expression with two terms is a binomial , and an expression with three terms is a trinomial . An expression with more than three terms is named simply by its number of terms—“five-term polynomial.”

You have learned the order of operations, commonly called PEMDAS. In other words, arithmetic operations are performed in the following order:

  1. First any operations inside grouping symbols (P).
  2. Second any values with exponents (E).
  3. Third multiplication and division in order from left to right (M and D).
  4. Finally addition and subtraction in order from left to right (A and S).

When we consider expressions, we can evaluate an expression for a given value. In other words, we can find the total value if we know how much the variable is. We can replace the variable(s) with the given value and then use the order of operations to calculate the total value.

Take a look at this one.

Evaluate x^2+3x-10 for x=5

Step 1: Replace the variables with the given value, 5.

5^2+3 \cdot 5-10

Step 2: Find the total value using the order of operations.

 & 5^2+3 \cdot 5-10\\& 25+3 \cdot 5-10 && (\text{There is no group, so first is the number with the exponent.})\\& 25+15-10 && (\text{Complete the multiplication})\\& 40-10 && (\text{Addition and subtraction from left to right.})\\& 30 && (\text{Our total is} \ 30.)

This is our answer. We can evaluate any expression when we have been given a value for the variable.

Evaluate each expression by using the given value.

Example A

Evaluate x^2+5x-1 for x=3

Solution: 23

Example B

Evaluate x^2+4x-9 for x=2

Solution: 3

Example C

Evaluate 2x^2+2x+5 for x=3

Solution: 29

Now let's go back to the dilemma from the beginning of the Concept.

Now you can use the formula and the given information to solve for the surface area of the cube. The given length of the cube is 8 feet. You can substitute this into the formula for the side length.

A &= 6s^2\\A &=6(8^2)\\A &=6(64)\\A &=384 \ sq.feet

This is the surface area of the cube.

Guided Practice

Here is one for you to try on your own.

Evaluate 4x^2+2x+15 for x=3


First, substitute the given value into the expression for x .


Next, simplify according to the order of operations.




Our answer is 57 .

Video Review

Explore More

Directions: Evaluate the following expressions for the given value.

  1. 7x^3 for x=2
  2. 6x^2 for x=3
  3. 4x^3 for x=2
  4. 8x^2 for x=2
  5. 10xy for x=2,y=3
  6. 7x^2+4x for x=2
  7. 6x^2+5x for x=2
  8. 3x^2+8x for x=3
  9. 7x^2+4x-2 for x=2
  10. 9x^2+5x-3 for x=3
  11. 5x^2+5x-2 for x=2
  12. 12x^2+8x+11 for x=2
  13. 6y^2-2y-8 for y = 6
  14. 3(x-7) + 5(x + 1) for x = 10
  15. -2y^3+6(y-4)+y for y = -3

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Date Created:

Mar 19, 2013

Last Modified:

Feb 26, 2015
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