List questions from irreducible-polynomials

Published on 01 Nov 2014 - 9:38

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Prove that some bivariate polynomial is irreducible

Published on 02 Nov 2014 - 6:29

211

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Irreducibility of an integer polynomial with exponents in linear sequence?

Published on 27 Mar 2026 - 23:57

456

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prove that $p(x)$ is an irreducible polynomial over $K$

Published on 03 Nov 2014 - 18:35

897

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Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$

Published on 06 Nov 2014 - 4:45

104

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Irreducible polynomial over $\mathbb F_5$

Published on 06 Nov 2014 - 6:45

91

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Factoring Real and Complex polynomials.

Published on 06 Nov 2014 - 14:06

1.4k

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Show that $f(x)=g(x^{p^e})$ and each root has the same multiplicity

Published on 06 Nov 2014 - 23:38

92

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Show that $\mathbb{Z}_3(a)$ is a splitting field of the polynomial

Published on 26 Mar 2026 - 6:29

203

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Find the degree of field extension

Published on 07 Nov 2014 - 1:42

444

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Reducible in $R[X]$ implies reducibility in $(R/I)[X]$

Published on 07 Nov 2014 - 4:53

177

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Irreducibility of a family of integer polynomials

Published on 08 Nov 2014 - 0:10

1k

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If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Published on 23 Feb 2026 - 1:08

572

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Irreducible polynomials in two and four variables

Published on 11 Nov 2014 - 1:56

44

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The number of bijective polynomials of particular degree in a field

Published on 11 Nov 2014 - 14:33

List Question

How to prove that $X^4+8X^3+X^2+2X+5$ is irreducible?

Prove that some bivariate polynomial is irreducible

Irreducibility of an integer polynomial with exponents in linear sequence?

prove that $p(x)$ is an irreducible polynomial over $K$

Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$

Irreducible polynomial over $\mathbb F_5$

Factoring Real and Complex polynomials.

Show that $f(x)=g(x^{p^e})$ and each root has the same multiplicity

Show that $\mathbb{Z}_3(a)$ is a splitting field of the polynomial

Find the degree of field extension

Reducible in $R[X]$ implies reducibility in $(R/I)[X]$

Irreducibility of a family of integer polynomials

If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Irreducible polynomials in two and four variables

The number of bijective polynomials of particular degree in a field

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