Can I use Eisenstein's criterion to show $x^{4}-2x^{3}+2x^{2}+x+4$ is reducible over $\mathbb{Q}$?
114529
Factoring/Reducing a polynomial $x^4 -2x^3 + 2x^2 + x + 4$
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
118950
Irreducibility criteria for polynomials with several variables.
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
70581
Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
53701
Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$
35959
irreducibility of a polynomial over $\mathbb{F}_2$
37731
An application of Eisenstein's criterion
154373
How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
53432
What is the algebraic closure of $\mathbb F_q$?
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$