Answer
quotient $5x^2+4x+11$ and remainder $r(x)=\frac{33}{x-2}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified as $\{5,-6,3 11\}$ and the divisor as $x-2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{5x^3-6x^2+3x+11}{x-2}=5x^2+4x+11+\frac{33}{x-2}$ with the quotient as $5x^2+4x+11$ and the remainder as $r(x)=\frac{33}{x-2}$
