Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - Chapter 3 Test Prep - Review Exercises - Page 399: 41

Answer

(a) see explanations. (b) see explanations.

Work Step by Step

(a) Use synthetic division, divide $f(x)$ by $x-1$ as shown in the figure (top half). We can see that all numbers in the bottom row of the division are nonnegative. Based on the Boundedness theorem, $f(x)$ has no zero greater than $1$. (b) Similarly, divide $f(x)$ by $x+3$ as shown in the figure (lower half). We can see that the numbers in the bottom row of the division alternate in sign. Based on the Boundedness theorem, $f(x)$ has no zero less than $-3$.
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