List questions from irreducible-polynomials

Published on 05 Apr 2026 - 22:20

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Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $

Published on 19 Dec 2015 - 5:40

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TO check for irreducibility of given polynomial

Published on 20 Dec 2015 - 11:31

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Which one of these rings are isomorphic?

Published on 20 Dec 2015 - 21:35

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Which of the following is an irreducible factor of $x^{12}-1$ over $\mathbb Q$?

Published on 21 Dec 2015 - 18:32

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Showing that $f=x^2 + a$ and $g=x^2 + x + a$ are reducible and irreducible, respectively, in $F[x]$ with $F = \{0, 1, a, a^2\}$

Published on 13 Mar 2026 - 1:06

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$P(X) = X^6 - 11X^4 + 36X^2 - 36$ has a root in $\mathbb{Q}_p$ for every $p$

Published on 22 Dec 2015 - 15:24

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Decompose $x^4 + x^3 + 1$ into irreducible factors over $\mathbb{Z}_2$

Published on 24 Dec 2015 - 2:35

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Irreducible polynomial of degree $3$ and degree of extension

Published on 28 Mar 2026 - 3:27

881

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Irreducible polynomial over $\mathbb{Q}$ can not have repeated root in $\mathbb{C}$

Published on 26 Dec 2015 - 1:46

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Generating irreducible polynomials over $GF(2)$

Published on 27 Dec 2015 - 20:48

112

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How many distinct roots within an algebraic closure

Published on 28 Dec 2015 - 12:23

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$p(x)$ irreducible polynomial $\iff J=\langle p(x)\rangle$ is a maximal ideal in $K[x]$ $\iff K[x]/J$ is a field

Published on 30 Dec 2015 - 5:58

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Irreducible polynomial $\; (x^2-2)^4-2$

Published on 31 Dec 2015 - 11:55

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A cubic polynomial over a field is irreducible if it has no roots

Published on 31 Dec 2015 - 16:16

List Question

Irreducibility of $f(x)=x^4+3x^3-9x^2+7x+27$

Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $

TO check for irreducibility of given polynomial

Which one of these rings are isomorphic?

Which of the following is an irreducible factor of $x^{12}-1$ over $\mathbb Q$?

Showing that $f=x^2 + a$ and $g=x^2 + x + a$ are reducible and irreducible, respectively, in $F[x]$ with $F = \{0, 1, a, a^2\}$

$P(X) = X^6 - 11X^4 + 36X^2 - 36$ has a root in $\mathbb{Q}_p$ for every $p$

Decompose $x^4 + x^3 + 1$ into irreducible factors over $\mathbb{Z}_2$

Irreducible polynomial of degree $3$ and degree of extension

Irreducible polynomial over $\mathbb{Q}$ can not have repeated root in $\mathbb{C}$

Generating irreducible polynomials over $GF(2)$

How many distinct roots within an algebraic closure

$p(x)$ irreducible polynomial $\iff J=\langle p(x)\rangle$ is a maximal ideal in $K[x]$ $\iff K[x]/J$ is a field

Irreducible polynomial $\; (x^2-2)^4-2$

A cubic polynomial over a field is irreducible if it has no roots

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