## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 2 - Test - Page 434: 18

#### Answer

$f(x)=2x^4-2$

#### Work Step by Step

Step 1. Given three zeros as $x=\pm1, i$, we can find all the 4 zeros as $x=\pm1,\pm i$ Step 2. Write the polynomial as $f(x)=c(x+1)(x-1)(x+i)(x-i)=c(x^2-1)(x^2+1)=c(x^4-1)$ where $c$ is a constant Step 3. Using the condition $f(3)=160$, we have $(3^4-1)c=160$, $80c=160$ and $c=2$ Step 4. We find the polynomial as $f(x)=2x^4-2$

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