Answer
quotient $6x^4+12x^3+22x^2+48x+93$ and remainder $r(x)=\frac{187}{x-2}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified as $\{6,0,-2,4 -3,1\}$ 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 $\frac{6x^5-2x^3+4x^2-3x+1}{x-2}=6x^4+12x^3+22x^2+48x+93+\frac{187}{x-2}$ with the quotient as $6x^4+12x^3+22x^2+48x+93$ and the remainder as $r(x)=\frac{187}{x-2}$
