Answer
$5x^{2}+4x+11+ \displaystyle \frac{33}{x-2}$
Work Step by Step
Dividing with $x-c\qquad...\qquad c=2.$
$\begin{array}{rrrrrr}
\underline{2}| &5 &-6 &3 &11 &\\
& &10 &8 &22 &\\
& --&--&--&--&\\
&5 &4 &11 &33 &\end{array}$
Quotient = $5x^{2}+4x+11$
Remainder = $33$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{5x^{3}-6x^{2}+3x+11}{x-2}$ = $5x^{2}+4x+11+ \displaystyle \frac{33}{x-2}$
