Polynomial Long Division Practice Test

Divide polynomials, track missing powers, interpret remainders, and verify results with division identities.

Polynomial Long Division Practice Test

20 polynomial long-division questions with quotient, remainder, and verification steps.

About This Polynomial Long Division Practice Test

This test focuses on the full divide–multiply–subtract–bring-down process used in polynomial long division. It includes divisors of degree one and two, exact divisions, nonzero remainders, and dividends with missing powers.

Several questions also test the division algorithm, quotient degree, reconstruction of a dividend, and the use of the Remainder Theorem to verify a result.

Skills Covered

Ordering polynomials, inserting zero placeholders, dividing leading terms, subtracting aligned powers, expressing quotient and remainder, and checking Dividend = Divisor·Quotient + Remainder.

Long-Division Process

  1. Write both polynomials in descending powers.
  2. Insert zero coefficients for missing powers.
  3. Divide leading terms, multiply back, and subtract.
  4. Stop when the remainder degree is smaller than the divisor degree.

Common Mistakes to Avoid

Do not misalign powers, stop while the remainder degree is still too large, lose signs during subtraction, or report only the quotient when a remainder remains.

Practice Format

Every solution states the quotient or remainder and explains the specific long-division error represented by each distractor.