How do you factorise a quadratic? Something like x^2 + 4x + 3

When factorising a quadratic the idea is to separate it into two brackets, so first, I usually write out the empty brackets like this; (x___)(x___) You then need to think of numbers that you can put in those brackets so that when you expand them you get the thing you started off with. The trick is that the numbers should add together to make the co-efficient of x (4 in this case) and multiply together to make the constant term (3 in this case). The best way is usually to think about the factors of the constant (3) and see if any of them add up together to make the x co-efficient (4). In this case +3 and +1 satisfy both conditions. The final step is to fill in the brackets with the numbers that work. In this case the answer would be; (x + 3)(x + 1) Note: Often the numbers that work will be negative so be careful.