Polynomial Irreducible in $\mathbb{F}_{2^i}$ for $i\leq{}6$

Question

Let $p(x)=x^4+x^3+1$ . Is $p$ irreducible in:

1) $\mathbb{F}_2$ ?

2) $\mathbb{F}_4$ ?

3) $\mathbb{F}_8$ ?

4) $\mathbb{F}_{16}$ ?

5) $\mathbb{F}_{32}$ ?

6) $\mathbb{F}_{64}$ ?

I can prove that $p$ is irreducible in $\mathbb{F}_2$ and $\mathbb{F}_4$ by showing it has no roots and no quadratic factors.

How can I complete questions 3-8?