- Topics At a Glance
- Exponents
- Negative Exponents
- Fractional Exponents
- Irrational Exponents
- Variables as Exponents
- Defining Polynomials
- Degrees of a Polynomial
- Multivariable Polynomials
- Degrees of Multivariable Polynomials
- Special Kinds of Polynomials
**Evaluating Polynomials**- Roots of a Polynomial
- Combining Polynomials
- Multiplying Polynomials
- Multiplication of a Monomial and a Polynomial
- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
- We'll Divide Polynomials Later!
- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

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.

Evaluate the polynomial 4*x*^{2} - 2*x* + 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 4 |

Example 2

If |

Exercise 1

Evaluate 5*x*^{2} - 3*x* - 4 for *x* = -1.

Exercise 2

Evaluate *x*^{4} - 16 for *x* = 2.

Exercise 3

3*x*^{3} + 4*x*^{2} - 5 for *x* = -3.

Exercise 4

Evaluate 3*xy* + 2*xy*^{2} - xy^{4} for *x* = 3, y = -2.

Exercise 5

Evaluate 4*x* + 3y - xy + 2*x*^{2}y for *x* = -1, y = -1.