Polynomial Remainder and Factor Theorems Worksheets

Before you begin

Factor polynomials, use exponent laws and solve equations with domain restrictions.

Worked example

Find the remainder when P(x) = x³ + 3x + 7 is divided by x − 2.

1. The remainder theorem says the remainder on division by x − c is P(c).
2. Evaluate P(2).

Answer: 21

Check your result using the method in the example before moving to the next question.

Choose your level

These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.

• Easy: Start with the preview and follow the worked example.
• Medium: Practice the same exercise types with a fresh numbered set.
• Hard: Use another set to practice explaining and checking your answers.

Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.

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Try six questions below, or choose a full set at your level.

Full worksheet sets

Practice next

• Factoring Higher-Degree Polynomials
• Polynomial Operations
• Zeros of Polynomials