Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 992: 3


The given statement is false.

Work Step by Step

In the synthetic division, the divisor must be in the form of $x-a$ which is a linear expression. Where,$x$ is a variable and $a$ is constant. The coefficient of the variable must be $1$. Consider an example: $\left( 3{{t}^{4}}+5{{t}^{3}}-8{{t}^{2}}-13t+2 \right)\div \left( {{t}^{2}}-5 \right)$ So, for this expression, the divisor $\left( {{t}^{2}}-5 \right)$ is not in the form of $x-a$. Hence, synthetic division cannot be used. This expression is solved by long division. So, long division can be used where synthetic division cannot be used but not vice-versa. Therefore, the given statement is false.
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