Question

for what values of k will x-4 be a factor of x^2+kx-52?

Answer 1

If $x-4$ is a factor of $x^2+kx-52$, then 4 is a root of $x^2+kx-52$.

So

$4^2+k\cdot4-52=0\\\\16+4k-52=0\\\\4k=36\\\\k=9$