Factorise x^2 + 8x + 12 (2017 non-calculator paper)

This question requires you to work through methodically in stages. We want two numbers, a and b, which fit into brackets of the form: (x + a)(x + b). By doing this, we have simplified the expression through factorisation. We can check we are correct at the end using the FOIL mathod of expansion. The coefficient of the x^2 term (number in front of x^2) is 1. The only factors of 1 are 1 and 1. Therefore, the brackets are (1x + a)(1x + b). This makes this question a little easier for us. Both a and b are positive numbers because both the x term (8x) and the constant term (12) are added (not subtracted) in the sequence. So we need two numbers which add to 8 and multiply to 12. By starting with factors of 12, our options are:1 and 12 or 2 and 6 or 3 and 4. The second combination, 2 and 6, is the only one wich adds to 8! This must be our answer. So we have (x + 2)(x + 6) as our final answer. Expanding this out using FOIL gives x^2 + 8x + 12 so we are correct.