List questions from irreducible-polynomials

203

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Polynomial of degree 5 that has no root in a normal extension, then it is irreducible over that extension

Published on 28 Mar 2026 - 11:21

49

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Minimal polynomial in $\mathbb{Q} [x]$

Published on 03 Jan 2020 - 4:59

207

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Is $x_0^4+x_1^4+x_2^4+x_3^4-ax_0x_1x_2x_3$ irreducible for every $a \in \mathbb{C}$?

Published on 27 Mar 2026 - 7:31

305

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Elements of $\mathbb{R}[x]/f$ for polynomial $f$ of degree $n$

Published on 05 Jan 2020 - 20:56

347

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$Y^3+XY^2+X^3Y+X$ is irreducible in $\mathbb{C}[X,Y]$

Published on 25 Mar 2026 - 6:12

477

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Confusion in proof of inseparable irreducible polynomial has zero derivative.

Published on 13 Jan 2020 - 22:15

63

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Show that a polynomial is irreducible

Published on 19 Jan 2020 - 15:37

195

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Is $x^{14}+x^7+1$ irreducible over $Q[x]$?

Published on 20 Jan 2020 - 4:26

167

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Is $x^2+y^2+z^2-xy-xz-yz$ reducible in $\mathbb{C}[x,y,z]$?

Published on 23 Jan 2020 - 19:21

91

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Factoring complex fourth degree polynomial into 2 irreducible real polynomials

Published on 23 Jan 2020 - 20:07

47

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Eliminating parameters from polynomial relations

Published on 23 Jan 2020 - 20:44

208

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GCD between an irreducible polynomial of degree $n$ in $\mathbb{F}_p[x]$ and $x^{p^n} - x$

Published on 24 Jan 2020 - 21:22

108

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How to show that $x^8 - x^7 + x^5 - x^4 + x^3 - x + 1$ is irreducible over $\mathbb{Z}$?

Published on 24 Jan 2020 - 21:57

176

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Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

Published on 28 Mar 2026 - 8:32

182

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Powers of roots satisfying irreducible polynomials form a basis for extension field

Published on 29 Jan 2020 - 1:31

List Question

Polynomial of degree 5 that has no root in a normal extension, then it is irreducible over that extension

Minimal polynomial in $\mathbb{Q} [x]$

Is $x_0^4+x_1^4+x_2^4+x_3^4-ax_0x_1x_2x_3$ irreducible for every $a \in \mathbb{C}$?

Elements of $\mathbb{R}[x]/f$ for polynomial $f$ of degree $n$

$Y^3+XY^2+X^3Y+X$ is irreducible in $\mathbb{C}[X,Y]$

Confusion in proof of inseparable irreducible polynomial has zero derivative.

Show that a polynomial is irreducible

Is $x^{14}+x^7+1$ irreducible over $Q[x]$?

Is $x^2+y^2+z^2-xy-xz-yz$ reducible in $\mathbb{C}[x,y,z]$?

Factoring complex fourth degree polynomial into 2 irreducible real polynomials

Eliminating parameters from polynomial relations

GCD between an irreducible polynomial of degree $n$ in $\mathbb{F}_p[x]$ and $x^{p^n} - x$

How to show that $x^8 - x^7 + x^5 - x^4 + x^3 - x + 1$ is irreducible over $\mathbb{Z}$?

Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

Powers of roots satisfying irreducible polynomials form a basis for extension field

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