I'm trying to determine if $x^5 + 3x^2 - 7x - 1$ irreducible in $\mathbb{R}[x]$

It has no obvious rational roots.

We can't apply Eisentstein's criterion as there is no $p$ that divides $-1, 3$ and $7$.

We are not dealing with $\mathbb{Z}[x]$ so I can't define homomorphisms to $\mathbb{Z}\_p[x]$ and check that the factors in those rings have the same degrees.

So what else can I do to see if it is irreducible, or not?