New posts in Irreducible Polynomials

Finding $f\in\mathbb{Q}[x]$ such that $f(\sqrt{2}+\sqrt{3})=\sqrt{2}$ and $\deg(f)\leq 3$. What's wrong with my approach?

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Showing $f(t) = t^4 + 2t^2 + 9$ is reducible over $\Bbb Q$

Irreducible polynomials of degree greater than 4 over finite fields

$x^4+x^3+x^2+x+1$ irreducible over $\mathbb F_7$

Irreducibility test in a number field

Finding an irreducible polynomial of degree $n$ in $\mathbb Q[X]$ with real roots

Problem in the "proof" of Eisenstein's criterion on irreducibility.

Elementary proof of "irreducible polynomials remain irreducible over transcendental extension"?

How can I show that the polynomial $t^n-x$ is irreducible in $F(x)[t]$?