Factors of an irreducible polynomial over $GF(2^8)$

Question

Prove that the irreducible polynomial $f(x) = x^8 + x^4 + x^3 + x + 1$ for $GF(2^8) $

1. has no polynomial factors of degree 1
2. has no polynomial factors of degree 2
3. has no polynomial factors of degree 3
4. has no polynomial factors of degree 4

How would I go about proving this? I thought the fact that $f(x)$ is irreducible means that it has no factors...