Is the polynomial $x^{2k+1} - 7x^2 + 1$ irreducible over $\mathbb{Q}$ for every positive integer $k$ ?

It is irreducible for all positive integers $k \leq 800$.

Question. Is the polynomial $x^{2k+1} - 7x^2 + 1$ irreducible over $\mathbb{Q}$ for every positive integer $k$?

It is irreducible for all positive integers $k \leq 800$.