College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 387: 11


$R=8$ $x-2$ is not factor

Work Step by Step

$$f\left( x\right) =\left( x-c\right) q\left( x\right) +R$$ $$\Rightarrow f\left( c\right) =\left( c-c\right) q\left( x\right) +R$$ $$\Rightarrow R=f\left( c\right) $$ $$f\left( x\right) =4x^{3}-3x^{2}-8x+4=\left( x-2\right) {q}\left( x\right) +R$$ $$\Rightarrow R=f\left( 2\right) =4\times 2^{3}-3\times 2^{2}-8\times 2+4=8\neq 0$$ The Factor Theorem states that if $f(c) = 0,$ then $x - c$ is a factor. since $f(2)=8\ne0$, $x-2$ is not factor
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