Factor Theorem Practice Test
20 factor-theorem and remainder-theorem questions with worked solutions.
Use polynomial values to test factors, find remainders and parameters, and build or factor polynomials.
20 factor-theorem and remainder-theorem questions with worked solutions.
The factor theorem connects polynomial evaluation, division, roots, and factorization in one efficient principle.
The test covers checking factors, using the remainder theorem, finding parameters, synthetic division, quotient polynomials, roots, constructing factored forms, and interpreting polynomial values.
You will evaluate P(a), interpret zero and nonzero remainders, find missing coefficients, identify linear factors, divide by known factors, and construct polynomials from zeros.
Typical mistakes include testing the wrong sign, confusing the input with the remainder, arithmetic errors with negative powers, and assuming a factor without verifying P(a)=0.
Use this free 20-question test for classroom review, tutoring, homework support, exam preparation, or independent practice. Each response is followed by an explanation, and the test can be repeated without registration.