Irreducibility of polynomials with random multiplicative coefficients revisited

We show that for a random polynomial $$F(X)=\sum _{n=1}^{N}f(n)X^{n-1},$$ where $f(n)$ is a random completely multiplicative function taking values in $\{\pm 1\}$, one has $$\underset{N\to \mathrm{\infty }}{\mathrm{lim\hspace{0.17em}sup}}\mathbb{P}[F(X)\text{ is irreducible}]=1.$$