Answer
quotient $x^2+x-3$ and remainder $r(x)=\frac{-12}{x^2+x-2}$
Work Step by Step
Step 1. Using long division as shown in the figure, we can obtain $\frac{x^4+2x^3-4x^2-5x-6}{x^2+x-2}=x^2+x-3+\frac{-12}{x^2+x-2}$
Step 2. We can identify the quotient as $x^2+x-3$ and the remainder as $r(x)=\frac{-12}{x^2+x-2}$
