Remainder Theorem & Factor Theorem: Definition & Examples


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question 1 of 3

Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4.

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Use the Factor Theorem to determine which expression is a factor of the following polynomial:

f(x) = x^3 - 2x^2 - 31x - 28.

2. Which example correctly illustrates the Factor Theorem?

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About This Quiz & Worksheet

This quiz and the accompanying worksheet will test your understanding of the remainder and factor theorems. You will be required to complete practice problems finding factors of polynomials and identifying examples of each theorem.

Quiz & Worksheet Goals

In this assessment, you will complete practice problems and identify examples relating to the following concepts:

  • Remainder theorem
  • Factor theorem
  • Determining the factors of a polynomial

Skills Practiced

This quiz and worksheet allow students to test the following skills:

  • Making connections - use understanding of the remainder and factor theorems to identify the next step in determining whether a given expression is a factor of a given polynomial
  • Problem solving - use acquired knowledge to solve remainder and factor theorem practice problems involving polynomials
  • Interpreting information - verify that you can view information and then use it to identify examples that illustrate the remainder or factor theorems.

Additional Learning

To learn more about finding factors of polynomials, see the associated lesson, Remainder Theorem & Factor Theorem: Definition & Examples which covers:

  • The procedure for division
  • Remainder theorem
  • Factor theorem
  • Finding remainders and factors of polynomials