# 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 + x2 – xy3?

#### 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.