Answer
$4x^3-9x^2+7x-6$.
Work Step by Step
The given expression can be written:
$(22x-24+7x^3-29x^2+4x^4)(x+4)^{-1}$
$=(22x-24+7x^3-29x^2+4x^4)\div(x+4)$
Rewrite the dividend in descending powers of $x$.
$\Rightarrow (4x^4+7x^3-29x^2+22x-24)\div(x+4)$
The value of $c$ is $-4$.
Use synthetic division to divide the polynomial $4x^4+7x^3-29x^2+22x-24$ by $x-c=x-(-4)$:
$\begin{matrix}
-4) &4&7&-29&22&-24 \\
& &-16&36&-28 &24\\
& --&--&--& --&--\\
& 4&-9&7&-6&0
\end{matrix}$
The quotient is $4x^3-9x^2+7x-6$ and the remainder is zero.
Hence, the solution is $4x^3-9x^2+7x-6$.
