New posts in Irreducible Polynomials

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

Let $f(x)= x^3+ax^2+bx+c \in \mathbb{Q}[x]$. Show that the splitting field of $f$ over $\mathbb{Q}$ has degree 1, 2, 3 or 6 over $\mathbb{Q}$.

How to factor this polynomial?

Why is $x^4-3x^2+18$ irreducible over the $3$-adics?

Minimal polynomial of $\alpha + \beta$ over $\mathbb{Q}$

Polynomial $x^3-2x^2-3x-4=0$

Proving a polynomial divides other polynomials

If $N$ is large enough, then $x^5-Nx+1$ and $x^5-Nx^2+1$ are irreducible over $\mathbb{Q}$.

Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

Is $x^6 + 108$ irreducible over $\mathbb{Q}$?