Answer
Quotient $Q(x)=2x^3-5x^2+20x-80$ Remainder $R(x)=308$
Work Step by Step
$\frac{2x^4+3x^3-12}{x+4}$, dividing using synthetic division:
$\begin{array}{lllll}
\underline{-4}| &2& 3 & 0 & 0& -12& \\
& & -8&20&-80 & 320 & \\
\hline & & & & \\
&2& -5 & 20 & -80&308 &
\end{array}$
$(2x^4+3x^3-12)\div(x+4)=2x^3-5x^2+20x-80$ $+\frac{308}{x+4}$.
thus, Quotient is $Q(x)=2x^3-5x^2+20x-80$ and remainder is $R(x)=308$
