List questions from irreducible-polynomials

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A method to count the number of monic irreducible polynomials of degree 2 or 3 or 4 in $\mathbb F_{p}[x]$

Published on 08 Mar 2017 - 0:43

1.5k

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Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?

Published on 08 Mar 2017 - 8:45

56

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Prove that the following polynomials are irreducible:

Published on 09 Mar 2017 - 7:54

942

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Prove that the polynomials are irreducible on F5[x,y]

Published on 09 Mar 2017 - 8:23

89

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Cannot factorise this polynomial into irreducibles

Published on 10 Mar 2017 - 13:17

15.1k

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Polynomial is irreducible over $\mathbb{Q}$

Published on 11 Mar 2017 - 3:54

258

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Are linear polynomials like this irreducible?

Published on 11 Mar 2017 - 15:02

3.8k

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Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$

Published on 12 Mar 2017 - 4:05

51

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Irreducibility over $\mathbb{F}_5$

Published on 12 Mar 2017 - 18:02

572

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Irreducible polynomial over field of characteristic $0$ cannot have multiple zeroes

Published on 13 Mar 2017 - 17:47

495

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Zeroes of irreducible polynomial over splitting field

Published on 27 Mar 2026 - 6:17

169

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Irreducible polynomial that has a multiple zero example

Published on 14 Mar 2017 - 21:20

445

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Minimal polynomial over some different fields

Published on 15 Mar 2017 - 4:37

865

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show it is irreducible over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(i)$

Published on 15 Mar 2017 - 17:35

420

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Find all irreducible factors of $x^{10}-1$ in $\mathbb{Z}_3[x]$

Published on 15 Mar 2017 - 20:46

List Question

A method to count the number of monic irreducible polynomials of degree 2 or 3 or 4 in $\mathbb F_{p}[x]$

Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?

Prove that the following polynomials are irreducible:

Prove that the polynomials are irreducible on F5[x,y]

Cannot factorise this polynomial into irreducibles

Polynomial is irreducible over $\mathbb{Q}$

Are linear polynomials like this irreducible?

Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$

Irreducibility over $\mathbb{F}_5$

Irreducible polynomial over field of characteristic $0$ cannot have multiple zeroes

Zeroes of irreducible polynomial over splitting field

Irreducible polynomial that has a multiple zero example

Minimal polynomial over some different fields

show it is irreducible over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(i)$

Find all irreducible factors of $x^{10}-1$ in $\mathbb{Z}_3[x]$

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