List questions from irreducible-polynomials

Published on 29 Mar 2026 - 2:12

62

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Factorise $x^5-x$ in $\mathbb{C}[x]$ and $\mathbb{R}[x]$

Published on 26 Mar 2023 - 12:39

147

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If $G_f\cong D_5$ for $f(x)=x^5+ax+b\in \mathbb{Q}[x]$, show that these criteria are true.

Published on 26 Mar 2026 - 17:33

107

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$1+X+⋯+X^{p−1}$ is not a product of two non-constant polynomials with nonnegative coefficients, where $p$ is prime.

Published on 30 Mar 2023 - 17:43

192

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why is $x^6-x^5 + x^3 - x^2 + 1$ irreducible over $\mathbb{Z}[x]$?

Published on 01 Apr 2023 - 13:23

100

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Conjecture, a monic polynomial with integer coefficients cannot have exactly one non-real root outside the open unit disk

Published on 25 Mar 2026 - 6:08

79

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Show that $Tr(A)$ is in the spectrum of $A+I$

Published on 25 Mar 2026 - 23:39

65

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Is $g(x)$ reducible in $k[x]$?

Published on 27 Mar 2026 - 12:28

131

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Irreducibility on homogeneous polynomials

Published on 09 Apr 2023 - 22:36

258

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How to factor a polynomial quickly in $\mathbb{F}_5[x]$

Published on 12 Apr 2023 - 16:05

109

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Showing that the polynomial $x^n+y^n-1$ is irreducible over $\mathbb{C}[x,y]$

Published on 15 Apr 2023 - 20:06

114

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Prove that $1+x+x^2+\dots+x^6$ is irreducible over $\Bbb Q[x]$

Published on 01 Apr 2026 - 8:27

92

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Prove the divisibility of the polynomial $x f'(x) - n f(x)$

Published on 19 Apr 2023 - 14:57

67

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Roots of $x^4+x^3+x^2+x+1$ over $\mathbb{Z}_3[x]/(x^3-x+1)$.

Published on 21 Apr 2023 - 9:57

31

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Evaluating an irreducible polynomial in a trascendental element

Published on 27 Apr 2023 - 10:06

List Question

length of $\mathbb{C}[x]/(x^{50}+x+1)\mathbb{C}[x]$ as a $\mathbb{C}[x]$-module

Factorise $x^5-x$ in $\mathbb{C}[x]$ and $\mathbb{R}[x]$

If $G_f\cong D_5$ for $f(x)=x^5+ax+b\in \mathbb{Q}[x]$, show that these criteria are true.

$1+X+⋯+X^{p−1}$ is not a product of two non-constant polynomials with nonnegative coefficients, where $p$ is prime.

why is $x^6-x^5 + x^3 - x^2 + 1$ irreducible over $\mathbb{Z}[x]$?

Conjecture, a monic polynomial with integer coefficients cannot have exactly one non-real root outside the open unit disk

Show that $Tr(A)$ is in the spectrum of $A+I$

Is $g(x)$ reducible in $k[x]$?

Irreducibility on homogeneous polynomials

How to factor a polynomial quickly in $\mathbb{F}_5[x]$

Showing that the polynomial $x^n+y^n-1$ is irreducible over $\mathbb{C}[x,y]$

Prove that $1+x+x^2+\dots+x^6$ is irreducible over $\Bbb Q[x]$

Prove the divisibility of the polynomial $x f'(x) - n f(x)$

Roots of $x^4+x^3+x^2+x+1$ over $\mathbb{Z}_3[x]/(x^3-x+1)$.

Evaluating an irreducible polynomial in a trascendental element

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