Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 495: 40


$a.\quad n(n+1)$ $b.\quad $Always even.

Work Step by Step

a. Find the GCF $n^{2}=n\cdot n$ $n=n$ GCF=$n$. $n^{2}+n\qquad...$factor out the GCF $=n(n)+n(1)\qquad...$apply the Distributive Property. $=n(n+1)$ b. When n is even, both $n^{2}$ and $ n $ are even, so their sum is even. When n is odd, both $n^{2}$ and $n $ are odd, so their sum is even. Answer:Always even.
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