Remainder Theorem Worksheets

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

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) = 2x 3 − 5x 2 + 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) = 2x 3 − 5x 2 + 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.

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)

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