Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.4 - Factoring Trinomials - Exercise Set - Page 362: 85

Answer

$(x^3+3)(2x^3+5)$.

Work Step by Step

The given expression is $=2x^6+11x^3+15$ We can write $=2(x^3)^2+11x^3+15$ Substitute $x^3=u$. $=2(u)^2+11u+15$ Simplify. $=2u^2+11u+15$ Rewrite $11u$ as $6u+5u$. $=2u^2+6u+5u+15$ Factor. $=2u(u+3)+5(u+3)$ $=(u+3)(2u+5)$. Substitute back $u=x^3$. $=(x^3+3)(2x^3+5)$.
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