Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 185: 50



Work Step by Step

If $c$ is a zero of a function with multiplicity $b$ then $(x-c)^b$ is a “factor” of the function. We are given that the degree is $3$, and the zeros are $-2$ (multiplicity 2) and $4$ (multiplicity 1), hence $f(x)=a(x+2)^2(x-4)\\ f(x)=a(x^3-12x-16)$ If $a=1$, the function becomes $f(x)=x^3-12x-16$
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