I have an exam on Monday, and I am not sure about the following.

In the field F= Z5[x] / <x^3 - x^2 - 1> is x^3 - x^2 - 1 irreducible? If not list the irreducible factors.

I am thinking that in F every element is written as something + <x^3 - x^2 - 1> and therefore the polynomial cannot be irreducible because any factor must at least include a multiple of <x^3 - x^2 - 1> and is thus of the same degree.

But my gut tells me that the polynomial should be irreducible....

any help please?