I find it more so of a time sink than actually learning anything when factoring quadratic polynomials with a coefficient attached to $\displaystyle x^2$

For instance, for any given expression $\displaystyle Ax^2+bx+c$ we must find the factors of both A and C. Such is the case in the following expression

$\displaystyle 4x^2-4x-15

$

combinations to try

a.(4x+15)(x-1) b.(4x-15)(x+1)

c.(4x-1)(x+15) d.(4x+1)(x-15)

e.(4x+5)(x-3) f.(4x-5)(x+3)

g.(4x+3)(x-5) h.(4x-3)(x+5)

i.(2x+15)(2x-1) j.(2x-15)(2x+1)

k.(2x+5)(2x-3)l.(2x-5)(2x+3)

L. Is correct

This seems very long and extraneous, is there a more effective manner to factor such problems instead of having to produce a list of all possible combinations? I have a ti83 program that can do this for me, but I would rather not resort to it if it will hurt my math skills later down the road.

Many Thanks