Stuck with a Binomial using the Difference Quotient

The problem is:

$\displaystyle f(x)= -5+5x^2$

I already know that it will end as 10x (it's derivative by the way).

But using the difference quotient:

$\displaystyle \frac{f(x+h)-f(x)}{h}$

I'm told that,

$\displaystyle f(x)= -5+5x^2$

Can be written in the form

$\displaystyle Ah+Bx+C$

Using the Calculus short cuts. I find that "B" is (10) and I find that "C" is (0)

However I don't know what what "A" is.

And when I do it long hand, I get stuck at this point.

$\displaystyle \frac{5(2x^2+2xh+h^2)}{h}$

How do I get "10x" from that above and find "A"?