Question

Polynomial irreducibility and perfect square.

score 381 · Answer 1 · 2016-04-03 23:57:57

381

Views

Polynomial irreducibility and perfect square.

Published on 03 Apr 2016 - 23:57

score 538 · Answer 2 · 2016-04-05 16:09:08

538

Views

Decomposition of a polynomial in a field extension

Published on 05 Apr 2016 - 16:09

score 61 · Answer 3 · 2016-04-05 16:18:30

61

Views

Show that the polynomial $P = x^8-6x^3+ 2x^2+2$ is irreductible in $\mathbb{Q}[x]$

Published on 05 Apr 2016 - 16:18

score 356 · Answer 4 · 2026-02-23 13:41:34

356

Views

Ireducible polynomial over $\mathbb Z_4$

Published on 23 Feb 2026 - 13:41

score 326 · Answer 5 · 2016-04-05 22:25:08

326

Views

General Multiplication Algorithm for Finite Field of GF(p^m) for small values of p^m

Published on 05 Apr 2016 - 22:25

score 641 · Answer 6 · 2016-04-07 19:46:37

641

Views

Irreducible factorisation of polynomial over quotient field

Published on 07 Apr 2016 - 19:46

score 145 · Answer 7 · 2016-04-07 21:20:41

145

Views

Prove that $X^6 - 10X^3 +8$ is irreducible over $\mathbb{Q}$.

Published on 07 Apr 2016 - 21:20

score 370 · Answer 8 · 2016-04-07 23:53:40

370

Views

Proving irreducibility; What is this method and what is the logic behind it?

Published on 07 Apr 2016 - 23:53

score 235 · Answer 9 · 2016-04-08 12:30:20

235

Views

Find an irreducible polynomial of degree $21$ in $\mathbb{F}_2[x]$

Published on 08 Apr 2016 - 12:30

score 2k · Answer 10 · 2016-04-08 13:31:44

2k

Views

Is the converse of "Let $f\in\mathbb Z[x]$. If $f$ is reducible over $\mathbb Q$, then it is reducible over $\mathbb Z$" true?

Published on 08 Apr 2016 - 13:31

score 1.5k · Answer 11 · 2016-04-08 14:55:56

1.5k

Views

Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$

Published on 08 Apr 2016 - 14:55

score 90 · Answer 12 · 2026-03-28 08:42:14

90

Views

Find $\mathrm{Gal}(L, \mathbb{Q})$ and prove that $\sqrt[3]{3} \in L$

Published on 28 Mar 2026 - 8:42

score 154 · Answer 13 · 2026-03-28 08:40:11

154

Views

Normal closure $L$ of $K=\mathbb{Q}(\sqrt{10+3\sqrt{13}})$ and structure of $\mathrm{Gal}(L/\mathbb{Q})$

Published on 28 Mar 2026 - 8:40

score 276 · Answer 14 · 2016-04-08 17:09:56

276

Views

Irreducible polynomial - Find roots

Published on 08 Apr 2016 - 17:09

score 265 · Answer 15 · 2016-04-08 22:18:58

265

Views

Can we use Eisenstein's Irreducibility Criterion to show that $x^4+1$ is not reducible in Q?

Published on 08 Apr 2016 - 22:18

List Question

Polynomial irreducibility and perfect square.

Decomposition of a polynomial in a field extension

Show that the polynomial $P = x^8-6x^3+ 2x^2+2$ is irreductible in $\mathbb{Q}[x]$

Ireducible polynomial over $\mathbb Z_4$

General Multiplication Algorithm for Finite Field of GF(p^m) for small values of p^m

Irreducible factorisation of polynomial over quotient field

Prove that $X^6 - 10X^3 +8$ is irreducible over $\mathbb{Q}$.

Proving irreducibility; What is this method and what is the logic behind it?

Find an irreducible polynomial of degree $21$ in $\mathbb{F}_2[x]$

Is the converse of "Let $f\in\mathbb Z[x]$. If $f$ is reducible over $\mathbb Q$, then it is reducible over $\mathbb Z$" true?

Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$

Find $\mathrm{Gal}(L, \mathbb{Q})$ and prove that $\sqrt[3]{3} \in L$

Normal closure $L$ of $K=\mathbb{Q}(\sqrt{10+3\sqrt{13}})$ and structure of $\mathrm{Gal}(L/\mathbb{Q})$

Irreducible polynomial - Find roots

Can we use Eisenstein's Irreducibility Criterion to show that $x^4+1$ is not reducible in Q?

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