Answer
$-x^{3} - 6x^{2} - 36x - 36 - \frac{216}{x - 6}$
Work Step by Step
Since we are dividing by (x - 6) the zero of that x = 6 goes into the top left space.
$\hspace{0mm}\underline{6|}\hspace{10mm}-1\hspace{10mm}0\hspace{10mm}0\hspace{10mm}180\hspace{10mm}0$
$\hspace{28mm}\underline{-6\hspace{4mm}-36\hspace{4mm}-216\hspace{3mm}-216}$
$\hspace{15mm}-1\hspace{6mm}-6\hspace{4mm}-36\hspace{4mm}-36\hspace{3mm}\underline{|-216}$
Since the bottom right space has a -216, the remainder is -216.
