Answer
quotient $x^4+x^3+2x^2+2x+2$ and remainder $r(x)=0$
Work Step by Step
Step 1. The coefficients of the dividend can be identified in order as $\{1,0,1,0,0,-2\}$ and the divisor is $x-1$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^5+x^3-2}{x-1}=x^4+x^3+2x^2+2x+2+\frac{0}{x-1}$ with the quotient as $x^4+x^3+2x^2+2x+2$ and the remainder as $r(x)=0$
