## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

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

#### Answer

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