Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.3 - Multiplying and Factoring Algebraic Expressions - Exercises - Page 21: 27



Work Step by Step

From the two terms, we can factor out $(x^{3}+1)$ and $\sqrt{x+1}$ $...=(x^{3}+1)\sqrt{x+1}[1-(x^{3}+1)]$ $=(x^{3}+1)\sqrt{x+1}(-x^{3})$ $=-x^{3}(x^{3}+1)\sqrt{x+1}$ Note: For $x^{3}+1$ there is a special formula, the sum of cubes: $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$ so $x^{3}+1=(x+1)(x^{2}-x+1)$ The answer could be further factored: $-x^{3}(x+1)(x^{2}-x+1)\sqrt{x+1}$ but the sum of cubes is not covered in this section, so we leave the answer as it is.
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.