For degree 3 or larger if factoring by grouping isn't possible we need to use the rational roots theorem.
The rational roots theorem tells us that all of the zero must be the ratio of the factors constant term and the factors of the lead coeffient.
so our constant term n=-12 and our lead term is a=1.
the factors of negative twelve are (plus or minus) 1,2,3,4,6,12
So the possiblities for the rational zero's are
so checking some of them from our list....
if we evaluate at 3 we get
so x=3 must be a zero and (x-3) is a factor
using polynomial long division or synthetic division you get
this can be factored again...