Classify Polynomials by Degree

What “degree” means

The degree of a polynomial is the highest exponent of the variable in any term, after the expression is simplified. Only terms with a variable count toward the degree. A nonzero constant has degree 0.

How to classify it

1. Simplify first. Combine like terms and remove parentheses if needed.
2. Look for the largest exponent. Ignore coefficients; only the power of the variable matters.
3. State the degree clearly.
   • Degree 0: constant
   • Degree 1: linear
   • Degree 2: quadratic
   • Degree 3: cubic
   • Higher degrees can be named by their number or as polynomial of degree __

Important checks

• If terms cancel, the degree may change. For example, a highest-power term might disappear after simplification.
• Make sure the expression is actually a polynomial: exponents should be whole numbers, and variables should not be in denominators or radicals.
• If the polynomial has no variable at all, its degree is 0 unless it is the zero polynomial.

Quick self-check

After simplifying, scan every term and identify the largest exponent. If your classification matches that exponent, the answer is correct.