Answer
$ 3x^3+6x^2+10x+10$.
Work Step by Step
The given expression is
$(3x^4-2x^2-10x-20)\div(x-2)$
Rewrite as $(3x^4+0x^3-2x^2-10x-20)\div(x-2)$
The value of $c$ is $2$
Use synthetic division
$\begin{matrix}
2) &3&0&-2&-10&-20 \\
& &6&12&20&20 \\
& --&--&--& --&--\\
& 3&6&10&10&0
\end{matrix}$
The quotient is $3x^3+6x^2+10x+10$ and the remainder is $0$.
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow 3x^3+6x^2+10x+10+\frac{0}{x-2}$.
$\Rightarrow 3x^3+6x^2+10x+10$.
