How to Classify Polynomials by Degree

By Chance E. Gartneer

A polynomial is a mathematic expression that consists of terms of variables and constants. The mathematical operations that can be performed in a polynomial are limited; addition, subtraction and multiplication are allowed, but division is not. Polynomials also must adhere to nonnegative integer exponents, which are used on the variables and combined terms. These exponents help in classifying the polynomial by its degree, which aids in solving and graphing of the polynomial.

Rearrange the terms of the polynomial from greatest to least. For example, the polynomial is 2xy + 4x² + 6y³ +1 = 0 becomes 6y³ + 4x² + 2xy + 1 = 0.

Find the highest power of each variable in the expression. For this example, x has a power of 2 because of the term 4x², and y has a power of 3 because of the term 6y³.

Add the powers together to calculate the degree of the polynomial. For this example, 2 added to 3 results in 5. The degree of the polynomial is 5.

Tip

For polynomials with only one variable, the degree is the largest exponent.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.