Answer
$-x^{3}-2x+6=(x+1)(-x^{2}+x-3)+9$
Work Step by Step
Using synthetic division,
$\left.\begin{array}{l}
-1\lfloor \\ \\ \\ \end{array}\right.\begin{array}{rrrrr}
-1 &0 &-2 &6& \\\hline
&1 &-1 &3& \\\hline
-1&1 &-3 &9& \end{array}$
$Q(x)=-x^{2}+x-3,\quad R(x)=9$
In the form $P(x)=D(x)\cdot Q(x)+R(x),$
$-x^{3}-2x+6=(x+1)(-x^{2}+x-3)+9$
