List questions from irreducible-polynomials

Published on 02 Dec 2013 - 20:23

231

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Is this a generator of a cyclic group?

Published on 03 Dec 2013 - 8:01

617

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Showing $x^4-24x^2+4$ is irreducible over $\mathbb{Q}$

Published on 04 Dec 2013 - 6:18

130

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Basis of partial fractions with irreducible quadratic.

Published on 30 Mar 2026 - 4:57

80

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Unique Factorization

Published on 05 Dec 2013 - 2:18

6.2k

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Is $x^4+x+1$ irreducible in $\Bbb{Q}[x]$?

Published on 05 Dec 2013 - 16:24

156

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irreducibility of $m$th cyclotomic polynomial in $\mathbb Z[x]$ implies irreducibility in $\mathbb Q[x]$? (Ireland and Rosen)

Published on 27 Mar 2026 - 7:50

85

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rational roots of a cubic

Published on 06 Dec 2013 - 22:00

279

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How do you prove the irreducibility of this multivariate polynomial?

Published on 07 Dec 2013 - 23:37

153

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A problem in extension fields

Published on 08 Dec 2013 - 7:15

325

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Is the ideal generated by $X^4+1$ maximal in $\mathbb{R}[X]$?

Published on 08 Dec 2013 - 16:44

52

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Let F⊆K be fields and let f and g be polynomials in F[x]. If f is irreducible in K[x], show that it is irreducible in F[x].

Published on 09 Dec 2013 - 5:08

59

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Inversion in factor rings

Published on 09 Dec 2013 - 17:48

682

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Prove that a polynomial is irreducible over $\mathbb Z$

Published on 10 Dec 2013 - 12:14

201

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Splitting field of irreducible polynomial $f(x)=x^4 +ax^2+b$ over field with charactersitic not equal to 2

Published on 26 Mar 2026 - 13:02

List Question

Minimal polynomial of $2^{-1/5}$

Is this a generator of a cyclic group?

Showing $x^4-24x^2+4$ is irreducible over $\mathbb{Q}$

Basis of partial fractions with irreducible quadratic.

Unique Factorization

Is $x^4+x+1$ irreducible in $\Bbb{Q}[x]$?

irreducibility of $m$th cyclotomic polynomial in $\mathbb Z[x]$ implies irreducibility in $\mathbb Q[x]$? (Ireland and Rosen)

rational roots of a cubic

How do you prove the irreducibility of this multivariate polynomial?

A problem in extension fields

Is the ideal generated by $X^4+1$ maximal in $\mathbb{R}[X]$?

Let F⊆K be fields and let f and g be polynomials in F[x]. If f is irreducible in K[x], show that it is irreducible in F[x].

Inversion in factor rings

Prove that a polynomial is irreducible over $\mathbb Z$

Splitting field of irreducible polynomial $f(x)=x^4 +ax^2+b$ over field with charactersitic not equal to 2

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