Help solve an equation

Question

I'm preparing for the SAT and tripped over the following problem:

$(x-8)(x-k) = x^2 - 5kx + m$

"In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m? A) 8 B) 16 C) 24 D) 32 E) 40 " Can someone please explain how to solve it?

Answer 1

$(x-8)(x-k) = x^2 - (k+8)x + 8k = x^2 - 5kx + m$. Thus:

$k + 8 = 5k$, and $m = 8k$.

So: $k = 2$, and $m = 16$