Algebra 2 (1st Edition)

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

Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Skill Practice - Page 366: 19

Answer

$x^2+2x^2-1+\frac{1}{x-2}$

Work Step by Step

We have to perform the division $$\dfrac{f(x)}{x-a}=\dfrac{x^3-5x+3}{x-2}.$$ 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. $$\dfrac{x^3-5x+3}{x-2}=x^2+2x^2-1+\dfrac{1}{x-2}.$$ The table built in the given solution is correct. What is wrong is the way it was read to give the result: the quotient has one degree less than $f$, therefore it would be $x^2+2x-1$, while the last number from the last line of the table represents the reminder. The correct result is: $$x^2+2x^2-1+\dfrac{1}{x-2}.$$
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