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: 41



Work Step by Step

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