How to factor trinomials of the form ax to the power of two +bc+c

(3x+1)(x+2). Since 3 is prime, you know the first terms in each set of parenthesis is 3 and 1 (or 1 and 3 it doesn’t matter). 2 is also prime, so you know the last terms are going to be 1 and 2 or 2 and 1. Since the trinomial only has plus signs, the factored version will also contain plus signs. If you notice that multiplying 3 and 2 gives you 6, and multiplying 1 and 1 gives you 1, and 1 + 6 is 7, you will see that the answer is (3x+1)(x+2). If for any reason you accidentally put the numbers in the wrong order, you can FOIL the equation to check that it equals the trinomial.