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`