I'm told that the "British" method is the most foolproof without having to continuously guess+check, and is very logical because I have trouble finding common factors and stuff in my head.

So for this problem:

x^2 + 11x + 12

I multiply 12 and 1 as per the method, and I get 12. Now I need to find two numbers that are multiples of 12 that add up to 11, and I can't find this.

So is there another different method that I can definitely get the answer with, foolproof without having to guess and check multiples as well? And what if ax^n, bx, and c are huge numbers? It'd be even more difficult using either British method or finding the GCF, right? And what if b or c is 0? Then the British method won't work at all.