z2 − z − 6

If you're wondering how to factorise this, then you need to think of two numbers that:

-> Multiply together and give you -6

-> Add together to give you -1

 

Eventually you can do it in your head, but for now it's probably easiest to write down all the whole numbers that multiply together to give you -6;

-1x6 = -6    1x-6 = -6

-2x3 = -6    2x-3 = -6

Now from these numbers which ones add together to give you negative one?

-3 + 2 = -1

So the two numbers you needed are 2 and -3.

Therefore it factorises into \(z^2-z-6 = (z+2)(z-3)\)