Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.2 Evaluate and Graph Polynomial Functions - 5.2 Exercises - Skill Practice - Page 341: 15

Answer

$f(3)=109$

Work Step by Step

We are given the polynomial $$f(x)=5x^3-2x^2-8x+16.$$ The polynomial value for $x=3$ is the remainder of the division of $f$ by $x-3$. We use synthetic division. First we write the coefficients of $f$ in order of descending coefficients and write the value at which $f$ is being evaluated to the left. Then we bring down the leading coefficient, multiply the leading coefficient by the $x$-value, write the product under the second coefficient, and add. Then we multiply the previous sum by the $x$-value, write the product under the third coefficient, and add. Perform this for all the remaining coefficients. We get the value of $f$ at the given $x$-value as the final sum. The final sum is $109$, therefore we got: $$f(3)=109.$$
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