Question

Constructing example of irreducible polynomial with distinct roots occurring with same multiplicity

score 76 · Answer 1 · 2026-04-13 19:31:29

76

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Constructing example of irreducible polynomial with distinct roots occurring with same multiplicity

Published on 13 Apr 2026 - 19:31

score 122 · Answer 2 · 2026-04-13 11:47:28

122

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Fields where for some $n$ all polynomials of degree $n$ are reducible but a degree $n+1$ irreducible exists

Published on 13 Apr 2026 - 11:47

score 53 · Answer 3 · 2026-04-13 15:58:51

53

Views

Irreducible polynomial of an element in a field

Published on 13 Apr 2026 - 15:58

score 75 · Answer 4 · 2026-04-13 22:43:55

75

Views

Seeing if a polynomial is irreducible over a field extension of $\Bbb Q$.

Published on 13 Apr 2026 - 22:43

score 411 · Answer 5 · 2022-02-22 18:55:18

411

Views

Proving $X^4 - 14X^2 + 9$ is irreducible

Published on 22 Feb 2022 - 18:55

score 264 · Answer 6 · 2026-04-10 07:00:04

264

Views

Finding the $\gcd$ of two polynomials over $\Bbb Z[x]$

Published on 10 Apr 2026 - 7:00

score 168 · Answer 7 · 2026-04-12 18:53:15

168

Views

Irreducibility of a degree $5$ polynomial

Published on 12 Apr 2026 - 18:53

score 102 · Answer 8 · 2022-03-02 13:00:24

102

Views

Monic irreducible polynomials in $\mathbb{F}_3[X]$

Published on 02 Mar 2022 - 13:00

score 296 · Answer 9 · 2022-03-03 06:10:16

296

Views

Irreducibility of $x^4+x+4$ over $\mathbb{F}_5$

Published on 03 Mar 2022 - 6:10

score 99 · Answer 10 · 2026-04-10 22:13:51

99

Views

Checking irreducibility by considering field extension

Published on 10 Apr 2026 - 22:13

score 72 · Answer 11 · 2022-03-06 12:13:20

72

Views

Difficulty understanding how $3x^2 + 12$ in $\mathbb{C}[x]$ is reducible.

Published on 06 Mar 2022 - 12:13

score 108 · Answer 12 · 2026-04-13 22:15:35

108

Views

Extension of an irreducible polynomial of degree $3$

Published on 13 Apr 2026 - 22:15

score 55 · Answer 13 · 2026-04-13 19:46:41

55

Views

Difficulty determining the number of irreducible factors in factorization of $x^{127} - 1$ over $\mathbb{Z}_2$.

Published on 13 Apr 2026 - 19:46

score 61 · Answer 14 · 2022-03-14 07:16:51

61

Views

How to prove the irreducibility $x^m+x^n+x+1$?

Published on 14 Mar 2022 - 7:16

score 44 · Answer 15 · 2022-03-15 14:13:21

44

Views

Find natural numbers $n, m \in \mathbb N, n$ odd, in which $\sqrt[n]m\notin\mathbb N$ but $x^n-m$ is not minimal polynomial in $\mathbb Q[x]$

Published on 15 Mar 2022 - 14:13

List Question

Constructing example of irreducible polynomial with distinct roots occurring with same multiplicity

Fields where for some $n$ all polynomials of degree $n$ are reducible but a degree $n+1$ irreducible exists

Irreducible polynomial of an element in a field

Seeing if a polynomial is irreducible over a field extension of $\Bbb Q$.

Proving $X^4 - 14X^2 + 9$ is irreducible

Finding the $\gcd$ of two polynomials over $\Bbb Z[x]$

Irreducibility of a degree $5$ polynomial

Monic irreducible polynomials in $\mathbb{F}_3[X]$

Irreducibility of $x^4+x+4$ over $\mathbb{F}_5$

Checking irreducibility by considering field extension

Difficulty understanding how $3x^2 + 12$ in $\mathbb{C}[x]$ is reducible.

Extension of an irreducible polynomial of degree $3$

Difficulty determining the number of irreducible factors in factorization of $x^{127} - 1$ over $\mathbb{Z}_2$.

How to prove the irreducibility $x^m+x^n+x+1$?

Find natural numbers $n, m \in \mathbb N, n$ odd, in which $\sqrt[n]m\notin\mathbb N$ but $x^n-m$ is not minimal polynomial in $\mathbb Q[x]$

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