Answer
$k=12$
Work Step by Step
If $x+3$ is a factor of $x^2-x-k$, then the remainder should be $0$ when performing
$$(x^2-x-k)\div(x+3)
.$$
Using the long division method below, then the remainder is $(-k+12)$. Since this remainder should be zero, then
$$\begin{aligned}
-k+12&=0
\\
k&=12
.\end{aligned}$$Hence, $x+3$ is a factor of $x^2-x-k$ if $k=12$.
