Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.4 - Division of Polynomials - Exercise Set - Page 445: 43

Answer

$\displaystyle \frac{3x^{4}+5x^{3}+7x^{2}+3x-2}{x^{2}+x+2}=3x^{2} +2x-1$

Work Step by Step

$ \begin{array}{llllllllll} & & 3x^{2} & +2x & -1 & & & \color{red}{ \small{Quotient}} & & \\ & & -- & -- & -- & -- & -- & -- & & \\ x^{2}+x+2 & ) & 3x^{4} & +5x^{3} & +7x^{2} & +3x & -2 & & & \\ & & 3x^{4} & +3x^{3} & +6x^{2} & & & \color{red}{\leftarrow \small{ 3x^{2}(x^{2}+x+2) } } & & \\ & & -- & -- & -- & & & \color{red}{\leftarrow \small{ subtract } } & & \\ & & & 2x^{3} & +x^{2} & +3x & -2 & & & \\ & & & 2x^{3} & +2x^{2} & +2x & & \color{red}{\leftarrow \small{2x(x^{2}+x+2) } } & & \\ & & & -- & -- & -- & & \color{red}{\leftarrow \small{ subtract }} & & \\ & & & & -x^{2} & -x & -2 & & & \\ & & & & -x^{2} & -x & -2 & \color{red}{\leftarrow \small{ -1(x^{2}+x+2) } } & & \\ & & & & -- & -- & -- & \color{red}{\leftarrow \small{ subtract } } & & \\ & & & & & & 0 & \color{red}{\leftarrow \small{ Remainder } } & & \end{array} $ $\displaystyle \frac{3x^{4}+5x^{3}+7x^{2}+3x-2}{x^{2}+x+2}=3x^{2} +2x-1$
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