Answer
Not a solution.
Work Step by Step
The given expression is
$=x^4-x^3-7x^2+x+6$
The value of $c$ is $4$
Use synthetic division
$\begin{matrix}
4) &1&-1&-7&1&6 \\
& &4&12&20&84 \\
& --&--&--& --&--\\
& 1&3&5&21&90
\end{matrix}$
The remainder is not zero.
Hence, the given solution is incorrect.