So firstly, you need to find two numbers that multiply to make 6 and add to make 5 Make a list of numbers that multiply to make 6 i.e. 1*6 and 3*2

So you can either have (x 6)(x 1) OR (x 3)(x 2)

Now you see that in x^{2} +5x+6, the 6 and 5 are both positive therefore there has to be an addition sign in both brackets therefore the only possibility is (x + 3)(x + 2) as if you used 6 and 1, their addition would make 7 which is not what we are looking for