Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 208: 44



Work Step by Step

Let us consider that $a$ is a zero of the function with multiplicity $b$. Then the factor of the function can be expressed as: $(x-a)^b$. We are given that the degree is $3$, and the zeros are $-4$, $0$ and $2$. Therefore, we can write the equation of the function as: $f(x)=a(x+4)(x-0)(x-2)\\=a(x^3+2x^2-8x)$ When $a=1$, the function can be written as: $f(x)=x^3+2x^2-8x$
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