How do you fully factorise this?

You need to apply the trial and error method.

Try x=1, x=2, x=3, x=4, x=5

When you try x=5, you should get 0.
So x-5 is the root. Then apply the long division method, so x³- 4x²- 11x +30 divide x-5.

Then you should find (x-5)(x²+x-6)
Factorise (x²+x-6)=(x-2)(x+3)

Therefore x³- 4x²- 11x +30 =(x-5)(x-2)(x+3)

Hope it helps and good luck.

factors of 30 that will add to -11 -5.-6

x-5 x^2+x-6

x*x^2=x^3
x*x=x^2
x*-6=-6x
-5*x*2=-5x^2
-5*x=-5x
-5*-6=30

x^3+x^2-5x^2-5x-6x +30
x^3-4x^2-11x+30

first of all, were you given a factor, such as (x-2) or something, would be helpful! if not, tommy is right...

no