Answer
$2x^2-3x+9$.
Work Step by Step
We can rewrite the given expression as division because $A^{-m}=\frac{1}{A^m}$.
$(9-x^2+6x+2x^3)(x+1)^{-1}=\frac{9-x^2+6x+2x^3}{x+1}$
Rewrite the dividend in descending powers of $x$.
$=(2x^3-x^2+6x+9)\div(x+1)$
Divide the polynomial $2x^3-x^2+6x+9$ by $x-c$, where $c=-1$, using synthetic division:
$\begin{matrix}
-1) &2&-1&6&9 \\
& &-2&3&-9 \\
& --&--&--& --\\
& 2&-3&9&0
\end{matrix}$
The quotient is $2x^2-3x+9$ and the remainder is zero.
Hence, the solution is $2x^2-3x+9$.
