Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 378: 53


a. $x=1,\pm4$ b. See graph and explanations.

Work Step by Step

a. Based on the graph, we can identify a zero as $x=-4$. Using synthetic division, we can find the quotient as $-x^2+5x-4$, as shown in the figure. Thus the zeros are $x=1,\pm4$ b. The end behaviors of the function can be found as $x\to-\infty, y\to\infty$ and $x\to\infty, y\to -\infty$ . The maximum number of turning points is $3-1=2$, and the y-intercept can be found as $y=f(0)=-16$. With the above information, we can finish the graph as shown in the figure, where the locations and values of the maximum and minimum are not a real concern at this point.
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