Question

$X^6 + 3X^4+3X^2-1$ is the minimal polynomial of $\sqrt{ \sqrt[3]{2}-1}$ over $\mathbb Q$

score 149 · Answer 1 · 2014-01-05 11:46:33

149

Views

$X^6 + 3X^4+3X^2-1$ is the minimal polynomial of $\sqrt{ \sqrt[3]{2}-1}$ over $\mathbb Q$

Published on 05 Jan 2014 - 11:46

score 1.3k · Answer 2 · 2014-01-05 17:21:17

1.3k

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How to prove that $f(x)=(x-1)^2(x-2)^2(x-3)^2\cdots(x-2013)^2+2014$ is reducible?

Published on 05 Jan 2014 - 17:21

score 113 · Answer 3 · 2014-01-05 17:22:53

113

Views

$Z^2-YZ-Y^2+X^2+2XY$ is an irreducible polynomial

Published on 05 Jan 2014 - 17:22

score 769 · Answer 4 · 2014-01-06 23:44:44

769

Views

Proving irreducibility via Eisenstein's criterion

Published on 06 Jan 2014 - 23:44

score 188 · Answer 5 · 2026-02-23 19:20:11

188

Views

Is $x^2 + 1$ irreducible over $\mathbb{Z}/_{3}[x]$?

Published on 23 Feb 2026 - 19:20

score 191 · Answer 6 · 2014-01-11 16:49:54

191

Views

Sufficient conditions for polynomial reducibility

Published on 11 Jan 2014 - 16:49

score 699 · Answer 7 · 2014-01-11 23:07:21

699

Views

If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?

Published on 11 Jan 2014 - 23:07

score 487 · Answer 8 · 2014-01-12 16:07:08

487

Views

Quick question about proving that $f(x)$ is irreducible over $D[x]$ if it is irreducible over $Q[x]$

Published on 12 Jan 2014 - 16:07

score 170 · Answer 9 · 2026-04-01 14:25:38

170

Views

Determine the number of divisors in $K[x]$ of $1 + x^{15}$ and of $1+x^{120}$

Published on 01 Apr 2026 - 14:25

score 439 · Answer 10 · 2014-01-13 14:16:15

439

Views

Check if polynomial is minimal over $\mathbb{Q}$

Published on 13 Jan 2014 - 14:16

score 134 · Answer 11 · 2014-01-14 20:47:40

134

Views

Irreducibility of $x^p - y^q$ in $K[[x,y]]$, for p,q>1 relatively prime

Published on 14 Jan 2014 - 20:47

score 110 · Answer 12 · 2014-01-16 11:19:10

110

Views

Why does $\mbox{Irr}(\alpha,K)$ have distinct roots in $N$?

Published on 16 Jan 2014 - 11:19

score 64 · Answer 13 · 2014-01-18 00:40:08

64

Views

Irreducible quadratic in $\mathbb{Z}_p$

Published on 18 Jan 2014 - 0:40

score 119 · Answer 14 · 2014-01-18 22:48:14

119

Views

Is $\cos x$ irreducible as a power series?

Published on 18 Jan 2014 - 22:48

score 911 · Answer 15 · 2026-03-27 12:20:19

911

Views

Beating Gauss on Irreducibility of Cyclotomic Polynomials?

Published on 27 Mar 2026 - 12:20

List Question

$X^6 + 3X^4+3X^2-1$ is the minimal polynomial of $\sqrt{ \sqrt[3]{2}-1}$ over $\mathbb Q$

How to prove that $f(x)=(x-1)^2(x-2)^2(x-3)^2\cdots(x-2013)^2+2014$ is reducible?

$Z^2-YZ-Y^2+X^2+2XY$ is an irreducible polynomial

Proving irreducibility via Eisenstein's criterion

Is $x^2 + 1$ irreducible over $\mathbb{Z}/_{3}[x]$?

Sufficient conditions for polynomial reducibility

If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?

Quick question about proving that $f(x)$ is irreducible over $D[x]$ if it is irreducible over $Q[x]$

Determine the number of divisors in $K[x]$ of $1 + x^{15}$ and of $1+x^{120}$

Check if polynomial is minimal over $\mathbb{Q}$

Irreducibility of $x^p - y^q$ in $K[[x,y]]$, for p,q>1 relatively prime

Why does $\mbox{Irr}(\alpha,K)$ have distinct roots in $N$?

Irreducible quadratic in $\mathbb{Z}_p$

Is $\cos x$ irreducible as a power series?

Beating Gauss on Irreducibility of Cyclotomic Polynomials?

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