Polynomial Division Worksheets
Free PDF · Problems + answer key · Instant download
Easy
10 problemsMedium
20 problemsHard
20 problemsMixed
30 problemsFree printable polynomial division worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from divide by (x − a), no remainder at the easy level through to divide by a quadratic at the advanced level.
What is polynomial division?
Polynomial division is the process of dividing one polynomial by another, similar to long division with numbers. Students learn two main methods: long division and synthetic division, both of which break down complex polynomial expressions into simpler quotients and remainders.
This skill is essential for factoring higher-degree polynomials, finding zeros of functions, and simplifying rational expressions in algebra and precalculus. Polynomial division also appears in calculus when working with partial fractions and in fields like engineering and computer science where algorithms process data using polynomial models.
Pick a difficulty
Click any level to open the generator with that difficulty pre-selected.
Beginner
Generate →- Concepts
- Divide by (x − a), no remainder
- Range
- roots −3 to 3
- Steps
- 2–3 steps
- Example
- (x² + 5x + 6) : (x + 2)
Easy
Generate →- Concepts
- Divide a cubic by (x − a), no remainder
- Range
- roots −4 to 4
- Steps
- 3–4 steps
- Example
- (x³ − 7x² − 6x + 72) : (x − 4)
Medium
Generate →- Concepts
- Division with a remainder
- Range
- roots −5 to 5
- Steps
- 3–5 steps
- Example
- (x³ + 2x² − x + 5) : (x − 1)
Hard
Generate →- Concepts
- Divide by a quadratic
- Range
- roots −5 to 5
- Steps
- 4–6 steps
- Example
- (x⁴ + 2x³ − 6x² − 3x + 18) : (x² + 2x − 2)
Try a sample problem
Try it right now
Click “Generate a problem” to see a fresh example of this technique.
Practice online → Interactive polynomial division problems with instant feedback.