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: 105

Answer

$(x^n+5)(2x^n+1)$

Work Step by Step

The product of the leading coefficient and the constant term is $2(5)=10$. The factors of 10 whose sum is equal to the coefficient of the middle term (which is 11) are 10 and 1. Rewrite the middle term using these factors to have: $\\2x^{2n}+11x^n+5 \\=2x^{2n}+10x^n+x^n+5 \\=(2x^{2n}+10x^n) + (x^n+5)$ Factor out the GCF of each group to have: $\\=2x^n(x^n+5)+1(x^n+5)$ Factor out the GCF of $x^n+5$ to have: $\\=(x^n+5)(2x^n+1)$
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