$\displaystyle a^2+a-12$

First, I see $\displaystyle a^2$, so I know the first factors must be $\displaystyle a$, and I see the last is a negative, so I know the signs are different

$\displaystyle a^2+a-12 = (a+?) (a-?)$

but what comes next? Do I have to try every combination of factors, and use FOIL until I find the correct combination? This is possible when I am working with these small numbers, because 12 only has a few factors (1*12,2*6,3*4), but what if it is made of larger numbers which could have dozens of different factors? It could take a whole day to finish a single problem.

This one is even more difficult, I also have to find the correct factors of 4

$\displaystyle 4x^2-8x-21$

Aren't there any tricks to make this more simple?