Show that $x^3 + 3x^2 + 9x + 3$ and $x^3 + 3x^2 + 3x − 4$ are irreducible in $\mathbb{Z}[x]$

Question

I need to show, as stated in the title, that $x^3 + 3x^2 + 9x + 3$ and $x^3 + 3x^2 + 3x − 4$ are irreducible in $\mathbb{Z}[x]$

I know that in case of second polynomial, if $f(x-1) = x^3 - 5$ which is irreducible, but i dont know how to form a solution from this.

Answer 1

First can be proved using Eisenstein's Criteria

Second You've already evaluated $f(x-1)$ correctly and since $f(x-1)$ is irreducible. So will be the case with $f(x)$. (why?)