Answer
$x+1$ is a factor of $f(x)$
Work Step by Step
$x+1$ is a factor of $f(x)$, if $f(-1)=0$
By subtituting $x$ by $-1$, we get:
$f(-1) = (-1)^3+6\times (-1)^2-2\times (-1) -7
\\f(-1) = 0$.
Therefore, $x+1$ is a factor. $f(x)$.