Remainder Theorem Worksheets

There are three sets of factor theorem and remainder theorem worksheets:

• Using Factor Theorem
  
• Using Remainder Theorem
  
• Divide Polynomials
  

Examples, solutions, videos, and worksheets to help Algebra II students learn about the remainder theorem and the remainder theorem.

How to use the Remainder Theorem to find the remainder when dividing a polynomial by a binomial?

There are two sets of remainder theorem worksheets

• Remainder theorem with cubic equations
• Remainder theorem with quartic or quintic equations

The Remainder Theorem is a fundamental concept in algebra that relates to polynomial functions and division. It states that when you divide a polynomial P(x) by a linear binomial of the form x − a, the remainder is equal to P(a).

In other words, if you have a polynomial P(x) and you want to find the remainder when it’s divided by x−a, you can substitute x = a into the polynomial P(x), and the result is the remainder of the division.

Here are the key steps to apply the Remainder Theorem:

1. Identify the polynomial P(x) and the linear binomial x−a.
2. Substitute the value of a into the polynomial P(x) and calculate P(a).
3. Interpret the result:
   If P(a)=0, then the remainder is 0, indicating that x−a is a factor of P(x).
   If P(a) ≠ 0, then the remainder is P(a).

The Remainder Theorem is particularly useful when you want to check whether a particular binomial is a factor of a polynomial or when you need to find the remainder of a polynomial division.

Example:
Suppose you have the polynomial P(x) = 2x³ − 5x² + 3x − 1 and you want to find the remainder when P(x) is divided by x − 2.

1. Identify the polynomial and the linear binomial.
   Polynomial: P(x) = 2x³ − 5x² + 3x − 1
   Linear binomial: x − 2
2. Substitute x = 2 into P(x):
   P(2) = 2(2)³ - 5(2)² + 3(2) − 1 = 16 − 20 + 6 − 1 = 1
3. Interpret the result:
   Since P(2)=1, the remainder when P(x) is divided by x−2 is 1.

Have a look at this video if you need to review how to use the remainder theorem.

• The Remainder Theorem

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Remainder Theorem Worksheets.

 

More Remainder Theorem Worksheets

Printable
(Answers on the second page.)
Remainder Theorem Worksheet #1 (cubic equations)
Remainder Theorem Worksheet #2 (quartic or quintic equations)

Online
Remainder Theorem

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Remainder Theorem
Solve Cubic Equations

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