I am trying to collect irreducible polynomials from a monic polynomial like x^n-1 in a field.

For example, n = 13 and the field is F_{3}, the monic polynomial is x^13-1. So far, I found I can use _factor()_ to get

FF.=GF(3)

x = PolynomialRing(FF,"x").gen()

factor(x^13-1)

(x + 2) * (x^3 + 2*x + 2) * (x^3 + x^2 + 2) * (x^3 + x^2 + x + 2) * (x^3 + 2*x^2 + 2*x + 2)

But I want to make each of them into a list, then from that list to get higher degree irreducible polynomials, such as
(x+2)(x^3+2*x+2),(x+2)(x^3+2*x+2)(x^3+2*x^2+2*x+2) and so forth.

can someone give me a hint or suggestion to do that? Thanks. I am not an English speaker, hope people can understand what I say.