I can tell you about the 'ac' method of factoring trinomials by way of an example:-
Factor 3x^2 - 4x - 15
first multiply the first number by the last That is 3 * -15 = -45
Now we need to find 2 factors of -45 which will when added give - 4 ( the coefficient of x)
-9 and = 5 look like the ones so we write
3x^2 - 9x + 5x - 15
Now factor this by grouping:-
= 3x(x - 3) + 5(x - 3)
x - 3 is common to the 2 parts so we have:-
(3x + 5)(x - 3) <-------- These are your factors
Any trinomial can be factored in this way.
