Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set: 41

Answer

$(x-1)(x^2+x+1)$

Work Step by Step

The given expression can be written as $x^3-1^3$, which is a difference of two cubes. RECALL: A sum or difference of two cubes can be factored using either of the following formulas: (1) $a^3+b^3=(a-b)(a^2-ab+b^2)$ (2) $a^3-b^3=(a-b)(a^2+ab+b^2)$ Using formula (2) above with $a=x$ and $b=1$ gives: $x^3-1=(x-1)(x^2+x(1)+1^2) = (x-1)(x^2+x+1)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.