Answer
Quotient $Q(x)=-x^2-7x-47$ Remainder $R(x)=-325$
Work Step by Step
$\frac{-x^3+2x+4}{x-7}$, dividing using synthetic division:
$\begin{array}{lllll}
\underline{7}| &-1& 0 & 2 & 4 & \\
& & -7&-49 & -329 & \\
\hline & & & & \\
&-1& -7 & -47 & -325 &
\end{array}$
$(-x^3+2x+4)\div(x-7)=-x^2-7x-47 $ $-\frac{325}{x-7}$.
thus, Quotient is $Q(x)=-x^2-7x-47$ and remainder is $R(x)=-325$
