query: Showing $x^4-16x^2+4$ is irreducible over $\mathbb{Q}$
positive_passages.docid: 26069
positive_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 103238
negative_passages.text: Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
negative_passages.docid: 77620
negative_passages.text: Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
negative_passages.docid: 85459
negative_passages.text: $x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
negative_passages.docid: 121479
negative_passages.text: Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
negative_passages.docid: 81377
negative_passages.text: Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
negative_passages.docid: 32054
negative_passages.text: How To Prove That The Rijndael Polynomial Is Irreducible?
negative_passages.docid: 8164
negative_passages.text: Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
negative_passages.docid: 31215
negative_passages.text: Irreducible cyclotomic polynomial
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 90144
negative_passages.text: Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 32391
negative_passages.text: Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
negative_passages.docid: 112427
negative_passages.text: Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
negative_passages.docid: 54192
negative_passages.text: Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
negative_passages.docid: 115782
negative_passages.text: Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
negative_passages.docid: 63605
negative_passages.text: Irreducible polynomials and affine variety