Factorise x^2 + 3x +2

You want two numbers that multiply to give 2 and add to give 3. Looking at factors is always easiest, so start by listing pairs of numbers that multiply together to give 2. There are only two such pairs, 1x2 and (-1)x(-2). The only pair that add together to make 3 is +1+2=3.

So the answer is (x+1)(x+2)