## Intermediate Algebra for College Students (7th Edition)

$x^{4}+x^{3}+2x^{2}+2x+2+\displaystyle \frac{3}{x-1}$
Dividing with $x-c\qquad...\qquad c=1.$ Don't forget to place 0's for the missing terms. $\begin{array}{rrrrrrrr} \underline{1}| &1 & 0 & 1 & 0 & 0 &1 \\ & & 1 & 1 &2 & 2 & 2 \\ & --& -- &-- &-- &-- &-- \\ &1 & 1 & 2 & 2 & 2 & 3 \end{array}$ Quotient = $x^{4}+x^{3}+2x^{2}+2x+2$ Remainder = $3$ $\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$ $\displaystyle \frac{x^{5}+x^{3}-2}{x-1}$ = $x^{4}+x^{3}+2x^{2}+2x+2+\displaystyle \frac{3}{x-1}$