Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.5 - Factoring Polynomials - Exercise Set: 138

Answer

$(x^n+4)(x^n+2)$

Work Step by Step

Let $u=x^n$ Then $u^2=x^{2n}$ Thus, the given expression, in terms of $u$, is: $=u^2+6u+8$ The leading coefficient of the trinomial is 1. This means that the trinomial can be factored by looking for factors of the constant term $(8)$ whose sum is equal to the coefficient of the middle term $(6)$. Note that: $8 = 4(2)$ and $4+2=6$ This means that the factors we are looking for are 4 and 2. Therefore the factors of the trinomial are: $u+4$ and $u+2$. Thus, $u^2+6u+8=(u+4)(u+2)$. Change the expression in terms of $x$ to obtain: $=(x^n+4)(x^n+2)$
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