query: A sufficient condition for irreducibility of a polynomial in an extension field.
positive_passages.docid: 27577
positive_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 64878
negative_passages.text: Is this polynomial irreducible in $\mathbb{Q}$?
negative_passages.docid: 132423
negative_passages.text: Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
negative_passages.docid: 79564
negative_passages.text: Algorithm to find the irreducible polynomial
negative_passages.docid: 18336
negative_passages.text: $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
negative_passages.docid: 70581
negative_passages.text: Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?
negative_passages.docid: 28658
negative_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 1487
negative_passages.text: How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
negative_passages.docid: 70537
negative_passages.text: Irreducible polynomials have distinct roots?
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 111347
negative_passages.text: Finding an example of field extensions satisfying certain properties
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 102432
negative_passages.text: Irreducible polynomial of degree $8$
negative_passages.docid: 7858
negative_passages.text: Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
negative_passages.docid: 76640
negative_passages.text: Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$