Clarification regarding hint given for showing $p(x)$ is irreducible over $\mathbb{Q}(\sqrt{-2})$.
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
10885
Existence of irreducible polynomials over finite field
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
134726
Show the polynomial is irreducible in $\textbf Z_2$
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
10627
When is $X^n-a$ is irreducible over F?
84355
Methods to see if a polynomial is irreducible
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
10821
Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$