Factorising Into Two Brackets

We may have to factorise expressions such as

When theterm is exactlyand not for example,this is very simple. We look for two numbers that add to give 7 and multiply to give 12. Two such numbers, the only two in fact are 3 and 4, hence the expression factorises as

If we have no minus signs, it is always as simple. If there are minus sign, as in the expressions

the the above paragraph changes very slightly. “ We look for two numbers that add to give 7 and multiply to give 12” becomes We look for two numbers that add or subtractto give -2 and multiply to give 8”. Two such numbers, the only two in fact, are 2 and 4.