So you need to put this expression in the form of:
(ax + p) (bx + c) where a, b, p and q are positive or negative numbers. such that when you expand the brackets (ie. both terms in the first brackets are multiplied with both terms in the second brackets) you get back your original expression.
So the clue is that we have to multiply ax and bx together to get 4x^2. So this could mean a = 1 and b = 4 or a = 2 and b = 2 or a = 4 and b = 1. Similarly, we much end up with a -9, this means p = 1 and q = -9 or p = -1 and q = 9 etc.
So we need a bit practice but if you play the options you will find that the factors are: (x - 1) (4x + 9). Why? Well, let's expand out the brackets:
x . 4x = 4x^2
x . +9 = +9x
- 1 . 4x = -4x
-1 . +9 = -9
Add them up: 4x^2 + 9x - 4x - 9 = 4x^2 +5x - 9
