Answer
$\displaystyle \frac{x^{4}-x^{3}-7x^{2}-7x-2}{x^{2}-3x-2}=x^{2} +2x+1$
Work Step by Step
$ \begin{array}{llllllllll}
& & x^{2} & +2x & +1 & & & \color{red}{ \small{Quotient}} & & \\
& & -- & -- & -- & -- & -- & -- & & \\
x^{2}-3x-2 & ) & x^{4} & -x^{3} & -7x^{2} & -7x & -2 & & & \\
& & x^{4} & -3x^{3} & -2x^{2} & & & \color{red}{\leftarrow \small{ x^{2}(x^{2}-3x-2) } } & & \\
& & -- & -- & -- & & & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & 2x^{3} & -5x^{2} & -7x & -2 & & & \\
& & & 2x^{3} & -6x^{2} & -4x & & \color{red}{\leftarrow \small{2x(x^{2}-3x-2) } } & & \\
& & & -- & -- & -- & & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & x^{2} & -3x & -2 & & & \\
& & & & x^{2} & -3x & -2 & \color{red}{\leftarrow \small{ +1(x^{2}-3x-2) } } & & \\
& & & & -- & -- & -- & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & & & & 0 & \color{red}{\leftarrow \small{ Remainder } } & &
\end{array} $
$\displaystyle \frac{x^{4}-x^{3}-7x^{2}-7x-2}{x^{2}-3x-2}=x^{2} +2x+1$
