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