## Algebra 1

Published by Prentice Hall

# Chapter 8 - Polynomials and Factoring - Mid-Chapter Quiz - Page 498: 16

#### Answer

$z^{3} - 5z^{2} + 13z - 9$

#### Work Step by Step

To simplify the polynomial we apply the distributive property that states: a(b+c)=ab+ac = $z(z^{2}-4z+9) - 1(z^{2}-4z+9)$ = ($z \times z^{2}$) + ($z \times -4z$) + ($z\times 9$) + ($-1 \times z^{2}$) + ($-1 \times -4z$) + ($-1 \times 9$) = $z^{3} - 4z^{2} + 9z - 1z^{2} + 4z - 9$ = $z^{3} - 1z^{2} - 4z^{2} + 9z + 4z - 9$ = $z^{3} - 5z^{2} + 13z - 9$ We add like terms to get final answer

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