Factorise: x^2+2x-3

think of it in the form of Ax^2 +Bx +C. Most of the GCSE examples will have A as zero so we will ignore the A. To factorise this you need to find what two numbers multiply to make C and adds to make B. In this case 3 is a prime number so the only numbers can be 3 or 1 but they can be odd or even. To find out if they are odd or even you look at the B value which is 2. The options are: 3+1, 3-1, 1-3, -1-3. The only one that makes +2 is 3-1. when factorising you have to change the signs when the numbers go in the brackets. so the answer is (x+3) (x-1) . To check your answer multiply this out and you should get what you started with.