Show that the following polynomial is irreducible over $\mathbb Q$:
$x^7 + 28x^2 + 32x + 6$
I know how to use the Eisenstein's Criterion method and testing with roots. The problem is that I can't use the methods here
For Eisenstein's Criterion I need a leading polynomial of degree higher than $1$
For the root method I need a polynomial of degree $2$ or $3$.
How can I solve the problem and what is the name of the method I should use?