I have to show that the following polynomials are irreducibles in $ \mathbb{Q}[X] $:
a) $ f(x) = x^p + (p-1) $
b) $\sum_{i=1}^{n}{a_ix^i}$ where $a_i \in \mathbb{Z}$ and there exist a prime $p$ such that $p \nmid a_0$, $p \mid a_i$ for each $i\ge 1$, and $p^2\nmid a_n$.
so for a) i used that $f(x)$ is irreducible iff $f(x+1)$ is, and then its easy to see that by Eisenstein $f(x+1)$ is irreducible.
I got stuck at b. i can't find how to change it in order to use Eisenstein (or maybe the solution is without Eisenstein?), can anyone help me please?
A polynomial
$$a_nx^n + ... + a_1x + a_0$$
is irreducible if and only if its reversal polynomial
$$a_0x^n + ... + a_{n-1}x + a_n$$
is irreducible.
Now you can use Eisenstein.