Answer
quotient $x^3-12x^2+73x-444$ and remainder $r(x)=\frac{2664}{x+6}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified in order as $\{1,-6,1,-6,0\}$ and the divisor is $x+6$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^4-6x^3+x^2-6x}{x+6}=x^3-12x^2+73x-444+\frac{2664}{x+6}$ with the quotient as $x^3-12x^2+73x-444$ and the remainder as $r(x)=\frac{2664}{x+6}$
