List questions from irreducible-polynomials

Published on 05 Mar 2021 - 17:00

265

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is it possible to find a monic quadratic polynomial that factors in Z but not in Z3?

Published on 08 Mar 2021 - 7:38

77

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Is the following polynomial reducible?

Published on 11 Apr 2026 - 22:35

107

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Find the inverse of $[f(z)=3z^2+z+3]$ in $\mathbb{Q}/(z^3-2z-2)$

Published on 09 Mar 2021 - 15:05

62

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Galois group of polynomial over $\mathbb{Q}(\sqrt{-3})$

Published on 01 Apr 2026 - 18:34

46

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Is there a matrix $A \in \mathbb{Q}^{n \times n}$ such that $P(A)=\mathbf{0}$, where $P$ is a monic polynomial with rational coefficients?

Published on 14 Mar 2021 - 20:07

52

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How do i check if a polynomial is irreducible?

Published on 09 Apr 2026 - 8:14

209

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Showing that $x^5 - 5 a^4 x + a$ is irreducible.

Published on 02 Apr 2026 - 20:55

97

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Are there irreducible polynomials of any degree over "most" fields?

Published on 12 Apr 2026 - 12:39

73

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Roots of polynomials that are the product of 2 polynomials

Published on 19 Mar 2021 - 14:51

79

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How to show that the polynomial $ab^3 + cd^3$ is irreducible?

Published on 12 Apr 2026 - 12:21

42

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Irreducible polynomial cannot have only perfect power values

Published on 11 Apr 2026 - 18:59

82

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How to show that $f(x) = 5x^{5}-8x^{4}+6x^{3}-4x^{2}+7x+9$ is irreducible over $\mathbb{Q}$?

Published on 24 Mar 2021 - 11:18

204

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Does Eisenstein's criterion apply when some coefficients are $0$?

Published on 12 Apr 2026 - 0:34

346

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Prove factor of $x^3-2$ is irreducible over $\mathbb{Q}(\sqrt[3]{2})$

Published on 24 Mar 2021 - 15:01

List Question

Show $f(x)=x^2+1$ is irreducible over $\mathbb{Q} (i\sqrt{2})$

is it possible to find a monic quadratic polynomial that factors in Z but not in Z3?

Is the following polynomial reducible?

Find the inverse of $[f(z)=3z^2+z+3]$ in $\mathbb{Q}/(z^3-2z-2)$

Galois group of polynomial over $\mathbb{Q}(\sqrt{-3})$

Is there a matrix $A \in \mathbb{Q}^{n \times n}$ such that $P(A)=\mathbf{0}$, where $P$ is a monic polynomial with rational coefficients?

How do i check if a polynomial is irreducible?

Showing that $x^5 - 5 a^4 x + a$ is irreducible.

Are there irreducible polynomials of any degree over "most" fields?

Roots of polynomials that are the product of 2 polynomials

How to show that the polynomial $ab^3 + cd^3$ is irreducible?

Irreducible polynomial cannot have only perfect power values

How to show that $f(x) = 5x^{5}-8x^{4}+6x^{3}-4x^{2}+7x+9$ is irreducible over $\mathbb{Q}$?

Does Eisenstein's criterion apply when some coefficients are $0$?

Prove factor of $x^3-2$ is irreducible over $\mathbb{Q}(\sqrt[3]{2})$

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