Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

6.3.5 Using the Factor Theorem

Algebra 16.3.5 Using the Factor Theorem
Search for key terms or text.

Cool Down

In all the division problems we completed that had a remainder of zero, we say that the divisor was a factor of the dividend.

Whenever a divisor, x−cx−c, divides a polynomial function, f(x)f(x), and results in a remainder of zero, we say x−cx−c is a factor of f(x)f(x).

This leads us to the Factor Theorem.

FACTOR THEOREM

For any polynomial function f(x)f(x),

  • if x−cx−c is a factor of f(x)f(x), then f(c)=0f(c)=0.
  • if f(c)=0f(c)=0, then x−cx−c is a factor of f(x)f(x).

Use the Factor Theorem to determine whether the binomial is a factor of the given polynomial function. Be prepared to show your reasoning.

1.

Is (x−5)(x−5) a factor of f(x)=x3−125f(x)=x3−125?

2.

Is (x−6)(x−6) a factor of f(x)=x3−216f(x)=x3−216?

3.

Is (x+3)(x+3) a factor of f(x)=x3+8x2+21x+18f(x)=x3+8x2+21x+18?

4.

Is (x+4)(x+4) a factor of f(x)=x3+x2−14x+8f(x)=x3+x2−14x+8?

PreviousNext
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.