Question

Proving Irreducibility of $x^4-16x^3+20x^2+12$ in $\mathbb Q[x]$

score 843 · Answer 1 · 2015-05-17 15:11:33

843

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Proving Irreducibility of $x^4-16x^3+20x^2+12$ in $\mathbb Q[x]$

Published on 17 May 2015 - 15:11

score 463 · Answer 2 · 2015-05-18 10:53:15

463

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Irreducible Polynomials over Finite Fields

Published on 18 May 2015 - 10:53

score 976 · Answer 3 · 2026-03-29 07:40:21

976

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Gauss's lemma: More than a stepping stone on the way to proving $R[x]$ is a UFD when $R$ is?

Published on 29 Mar 2026 - 7:40

score 573 · Answer 4 · 2015-05-20 04:26:13

573

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If some non-primitive polynomial in $\mathbb Z[x]$ is irreducible over $\mathbb Q$, does this imply it is irreducible over $\mathbb Z$?

Published on 20 May 2015 - 4:26

score 592 · Answer 5 · 2026-03-31 11:58:14

592

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Existence of Jordan decomposition over finite field

Published on 31 Mar 2026 - 11:58

score 18 · Answer 6 · 2015-05-23 04:22:40

18

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Factorizing polynomials: How to calculate $g_{(X)}\in F_{q}[x]$ if we have $f_{(x)} = g_{(x)}^p$

Published on 23 May 2015 - 4:22

score 77 · Answer 7 · 2015-05-24 03:23:26

77

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When does reducibility over $\mathbb{Z}_n$ imply reducibility over $\mathbb{Z}$

Published on 24 May 2015 - 3:23

score 135 · Answer 8 · 2015-05-24 12:27:59

135

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Is there a more efficient way of counting the number of reducible polynomials?

Published on 24 May 2015 - 12:27

score 2.2k · Answer 9 · 2015-05-25 21:23:38

2.2k

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Construction of addition and multiplication table for GF(4)

Published on 25 May 2015 - 21:23

score 145 · Answer 10 · 2015-05-25 22:41:18

145

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Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$

Published on 25 May 2015 - 22:41

score 385 · Answer 11 · 2015-05-26 00:41:27

385

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How to find the irreducible polynomial?

Published on 26 May 2015 - 0:41

score 2k · Answer 12 · 2015-05-26 09:26:18

2k

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Proof for quotient polynomial rings equivalent to field extension

Published on 26 May 2015 - 9:26

score 107 · Answer 13 · 2015-05-28 15:02:47

107

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irreducibility of polynomials made by perturbation from a polynomial

Published on 28 May 2015 - 15:02

score 1.2k · Answer 14 · 2015-05-29 02:40:51

1.2k

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Show that $x^{3}-3$ irreducible over $\mathbb{Q}(\sqrt{-3})$

Published on 29 May 2015 - 2:40

score 537 · Answer 15 · 2015-05-29 17:08:22

537

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Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$

Published on 29 May 2015 - 17:08

List Question

Proving Irreducibility of $x^4-16x^3+20x^2+12$ in $\mathbb Q[x]$

Irreducible Polynomials over Finite Fields

Gauss's lemma: More than a stepping stone on the way to proving $R[x]$ is a UFD when $R$ is?

If some non-primitive polynomial in $\mathbb Z[x]$ is irreducible over $\mathbb Q$, does this imply it is irreducible over $\mathbb Z$?

Existence of Jordan decomposition over finite field

Factorizing polynomials: How to calculate $g_{(X)}\in F_{q}[x]$ if we have $f_{(x)} = g_{(x)}^p$

When does reducibility over $\mathbb{Z}_n$ imply reducibility over $\mathbb{Z}$

Is there a more efficient way of counting the number of reducible polynomials?

Construction of addition and multiplication table for GF(4)

Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$

How to find the irreducible polynomial?

Proof for quotient polynomial rings equivalent to field extension

irreducibility of polynomials made by perturbation from a polynomial

Show that $x^{3}-3$ irreducible over $\mathbb{Q}(\sqrt{-3})$

Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$

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