How should I go about factorising x^2+5x+6?

I always think of the middle number as the sum and the last number as the product (in this example, we have the sum as 5 and the product as 6!) This just means that we have to look for two numbers which add together to equal the sum (5) and multiply together to give us the product (6). In this case our numbers are 3 and 2 (quick check: 3+2=5, 3x2=6... yes!) Now all that's left is to check which signs we should put infront of these numbers when we put them into brackets. This depends on the signs given within the quadratic, the second sign (+ before the 6) tells us that our two signs must be the same as eachother and the first sign (+ before the 5x) tells us that the signs are both plus! Hence, we now have everything we need to factorise the quadratic and our result is (x+3)(x+2)