Answer
quotient $2x^4-7x^3+15x^2-31x+64$ and remainder $r(x)=\frac{-129}{x+2}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified in order as $\{2,-3,1,-1,2,-1\}$ and the divisor is $x+2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{2x^5-3x^4+x^3-x^2+2x-1}{x+2}=2x^4-7x^3+15x^2-31x+64+\frac{-129}{x+2}$ with the quotient as $2x^4-7x^3+15x^2-31x+64$ and the remainder as $r(x)=\frac{-129}{x+2}$
