How do I factorise a quadratic equation?

To factorise an equation is to put it into (usually two) brackets in the form (x+a)(x+b), where a and b are integers, which multiply out to make the original equation. So whenever you see the word factorise, think brackets. It is easiest to explain using an example, for instance, factorise the equation x² + 5x + 6. X². First draw out two empty brackets like so (      )(         ) that we can fill in. First step is the x². x² is the same as X x X so we can put an x at the front of each bracket, as we know that they will have to multiply together to make the x² in the equation like so (x  )(x   ). Secondly, onto the numbers - we have to find two numbers that when multiplied together will make 6, and when added together will make 5. Do this in a logical order to avoid missing out any possible combinations- go through the factors of 6, testing each time if they will add up to 5. So, for the factors of 6 - 1x6=6 however 1+6=7 so 1 and 6 cannot be the numbers in our brackets. 2x3=6 and 2+3=5, in this case we have found our combinations of numbers to put in the brackets. As both brackets only contain one x it does not matter whether the 2 or 3 go in the first or second bracket. Also, in this example all terms in the equation are positive so both brackets will have a plus in them. So our factorised equation will look like this: (x+2)(x+3).