Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 81

Answer

$(x^3+3)(2x^3-3)$

Work Step by Step

The two numbers whose product is $ac= 2(-9)=-18 $ and whose sum is $b= 3 $ are $\{ 6,-3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2x^6+3x^3-9 $, is \begin{array}{l}\require{cancel} 2x^6+6x^3-3x^3-9 \\\\= (2x^6+6x^3)-(3x^3+9) \\\\= 2x^3(x^3+3)-3(x^3+3) \\\\= (x^3+3)(2x^3-3) .\end{array}
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