Factorise a^2 + a - 30

This is a quadratic equation in the form ax²+bx+c. As the three terms don't have a common factor we cannot factorise this into one bracket, instead we will factorise it into two. In order to do this we must find two numbers that multiply to give us -30 and add together to give us 1, as -30 is our c and 1 is our b. (ask student if they can come up with the numbers). The correct two numbers here would be +6 and -5 as these both multiply together to give -30 and add together to give 1. Therefore these are the two numbers we need to put in our two brackets and the answer is (x+6)(x-5). We can check this answer is correct by multiplying out the brackets again. (ask student to check).