Polynomials Practice Test

About This Polynomials Practice Test

This mixed review covers the major skills students use when working with polynomials. Questions range from vocabulary and standard form to operations, evaluation, composition, division, zeros, end behavior, and graph structure.

The set is designed as a broad diagnostic rather than a single-method drill, so students must decide which polynomial rule applies before calculating.

Skills Covered

Degree and leading coefficient, term classification, combining like terms, polynomial operations, function evaluation, composition, the Remainder Theorem, end behavior, and turning-point limits.

Key Rules

1. Add or subtract only like powers.
2. When multiplying monomials, multiply coefficients and add exponents.
3. The degree of a nonzero product is the sum of the factor degrees.
4. A degree-n polynomial has at most n−1 turning points.

Common Mistakes to Avoid

Do not add exponents when adding terms, lose subtraction signs across parentheses, or confuse a leading coefficient with the polynomial’s degree.

Practice Format

Every solution explains the selected operation and shows why each alternative answer fails.