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Polynomial Division

A free Algebra II lesson from the “Polynomial Division” unit, with a worked example and practice problems including step-by-step solutions.

Polynomial division rewrites one polynomial divided by another. For a monomial divisor, divide each term. Synthetic division is a compact method for dividing by x - c.

What you'll learn

Why it matters: Reducing a polynomial after finding one zero, simplifying transfer-function fractions, and computing remainders for engineering checks all use polynomial long or synthetic division. The process mirrors numerical long division, line by line.

Worked example

Problem. Divide (6x^3 + 9x^2) by 3x.

  1. Divide each term by 3x.
  2. 6x^3/3x = 2x^2.
  3. 9x^2/3x = 3x.

Answer: 2x^2 + 3x

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Divide 12x^3 by 3x.

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  1. 12/3 = 4 and x^3/x = x^2.

Answer: 4x^2

2. Divide (10x^2 + 5x) by 5x.

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  1. Divide each term by 5x.

Answer: 2x + 1

3. Divide (8x^4 - 4x^2) by 4x^2.

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  1. Divide each term.

Answer: 2x^2 - 1

4. When dividing by x - 3 using synthetic division, use...

Choices: 3 · -3 · 0 · x

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  1. x - c uses c.

Answer: 3

5. If dividing by x - 2 gives remainder 0, then x - 2 is a...

Choices: Factor · Degree · Coefficient · Constant only

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  1. Remainder 0 means exact division.

Answer: Factor

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