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: 46


$x^4-3x^3-15x^2+19x +30$

Work Step by Step

Let us consider that $a$ is a zero of the function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$. We are given that the degree is $4$, and the zeros are $-3$, $-1$, $2$, and $5$. Therefore, we can write the equation of the function as: $f(x)=(x+3)(x+1)(x-2)(x-5) \\=x^4-3x^3-15x^2+19x +30$
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