College Algebra (10th Edition)

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

Chapter R - Section R.6 - Synthetic Division - R.6 Assess Your Understanding - Page 61: 6



Work Step by Step

The fist row of the synthetic division shows $c$ and the coefficients of the dividend in descending order of degree. Thus, the synthetic division involves: $c=-2$ which means the divisor $x-c$ is $x-(-2) = x+2$ dividend = $5x^3+3x^2+x+1$ The last row of the synthetic division shows the quotient, with the degree of each term one lower than the dividend. The rightmost entry is the remainder. Thus, the quotient is $5x^2-7x+16$ with a remainder of $-31$. Therefore, the division and the quotient can be written as: $\dfrac{5x^3+3x^2+x+1}{x+2}=5x^2-7x+16+\dfrac{-31}{x+2}$ The given statement is true.
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