Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Lesson Check: 4

Answer

$y=x^3-x$

Work Step by Step

RECALL: If $c$ is a zero of a function, then $x-c$ is a factor of the function. The required function has the zeros -1, 1, and 0. This means that the function has the following factors $\\x-(-1) = x+1, \\x-1, \text{ and } x$. Thus, the function is $y=(x+1)(x-1)(x) \\y=(x^2-1)(x) \\y=x^3-x$.
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