Factor 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 factor theorem and the remainder theorem.

How to use the Factor Theorem to determine whether a binomial is a factor of the given polynomial?

There are two sets of factor theorem worksheets

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

To determine whether a given binomial is a factor of a polynomial, you can use the Factor Theorem. The Factor Theorem states that if a polynomial P(x) has a factor of the form x−a, then P(a)=0. In other words, if you substitute the value a into the polynomial and the result is zero, then (x−a) is a factor of the polynomial.

Here are the steps to determine whether a binomial is a factor:

1. Identify the binomial and the polynomial.
2. Use the Factor Theorem. Substitute the value from the binomial (let’s call it a) into the polynomial, and calculate P(a).
3. Interpret the result:
   If P(a) = 0, then the binomial (x−a) is a factor of the polynomial.
   If P(a) ≠ 0, then the binomial is not a factor of the polynomial.

Example:
Determine whether x+3 is a factor of the polynomial
x³ + 3x² + 3x + 9

1. Identify the binomial and the polynomial. Binomial: x+3 Polynomial: x³ + 3x² + 3x + 9
2. Use the Factor Theorem. Substitute a=-3 into P(x): P(3) = (-3)³ + 3(-3)² + 3(-3) + 9
3. Interpret the result: P(3) = -27 + 27 - 9 + 9 = 0 Since P(3)=0, this means that x+3 is a factor of the polynomial P(x).

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

• The Factor Theorem

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

 

More Factor Theorem Worksheets

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

Online
Remainder Theorem

Related Lessons & Worksheets

Factor Theorem
Solve Cubic Equations

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