## 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 496: 42

#### Answer

$a.\quad 3$ $b.\quad n-3$ $c.\displaystyle \quad \frac{1}{2}n^{2}-\frac{3}{2}n$ $d.\quad 20$

#### Work Step by Step

a. The polygon has six sides. From one vertex: three diagonals. b. It will have $n-3$ diagonals, \\ as we can not join the vertex with itself and its two neighboring vertices to form a diagonal. c. $\displaystyle \frac{n}{2}(n-3)\qquad...$apply the Distributive Property. $=\displaystyle \frac{n^{2}}{2}-\frac{3n}{2}$ $=\displaystyle \frac{1}{2}n^{2}-\frac{3}{2}n$ d. Substitute $n=8$ into the diagonal formula $D=\displaystyle \frac{8}{2}(8-3)\qquad...$apply the Distributive Property. $D=4\cdot 5$ $D=20$. The polygon has 20 diagonals

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