Remainder Theorem Practice Test

Evaluate polynomials at divisor zeros, find remainders, test factors, and determine unknown coefficients.

Remainder Theorem Practice Test

This test has 20 questions

About This Remainder Theorem Practice Test

The Remainder Theorem connects polynomial division by x−a with the single value f(a).

Problems include direct evaluation, divisibility tests, factor decisions, and finding parameters from a stated remainder.

Skills Covered

Polynomial evaluation, divisor zeros, remainders, Factor Theorem, unknown coefficients, and divisibility.

Key Ideas

  1. For x−a, evaluate f(a).
  2. For x+a, evaluate f(−a).
  3. A zero remainder proves the divisor is a factor.
  4. Set f(a) equal to the stated remainder when solving for a parameter.

Common Mistakes to Avoid

Do not substitute the sign appearing in the divisor without first solving the divisor equal to zero.

Practice Format

Each question has four answer choices. The explanation shows the method, completes the algebra, states the conclusion, and explains why every distractor is incorrect.