List questions from irreducible-polynomials

Published on 07 May 2021 - 9:29

104

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Show a polynomial is reducible over $F=\mathbb{Z}/(p)$ with $p$ prime and $p=a^2+b^2$

Published on 07 May 2021 - 10:37

46

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Show that a polynomial is irreducible on $\mathbb{Q}$

Published on 07 May 2021 - 20:49

86

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Prove: If $f,g \in \Bbb Z[x]$ then $C(fg) = C(f)C(g)$

Published on 29 Mar 2026 - 8:14

171

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Decompose in irreducible factors over $\mathbb{Z}_3[X]$

Published on 13 Apr 2026 - 1:39

62

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Degree of a polynomial zero over the simple extension attained by adjoining another zero.

Published on 12 Apr 2026 - 21:51

307

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If I erase one of the variables in an irreducible homogeneous polynomial, it's still irreducible

Published on 12 May 2021 - 5:56

97

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Show that $K(\sqrt{2\sqrt{2}-1})$ is a degree $4$ Abelian extension of $K=\Bbb Q (i\sqrt{14})$

Published on 12 May 2021 - 20:12

103

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Let $n\in\Bbb Z$ and let $f(x)=x^3-nx^2-(n+3)x-1$. Show that $f(x)$ is irreducible in $\Bbb Q[x]$.

Published on 14 May 2021 - 13:15

44

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The degree and minimal polynomial over $\mathbb{Q}$ of $j\sqrt{2}$

Published on 16 May 2021 - 5:51

80

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Study the irreducible of polynomial $P(X) = X^n + X + p$, with $p$ be a prime number and $n$ an integer $\geq 2$.

Published on 16 May 2021 - 18:17

139

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Power Series where partial sums are irreducible polynomials?

Published on 28 Mar 2026 - 0:06

141

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Irreducible polynomial divisible by all primes

Published on 23 May 2021 - 7:06

139

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The irreducibility of $X^3-X^2+1$ over $\mathbb{F}_9[X]$

Published on 24 May 2021 - 9:13

152

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If $p$ is irreducible, is $p(x^2)$ irreducible?

Published on 27 May 2021 - 18:55

List Question

Determining the reducibility of $x^4+2x-2$ in $\mathbb{F}_9[x]$

Show a polynomial is reducible over $F=\mathbb{Z}/(p)$ with $p$ prime and $p=a^2+b^2$

Show that a polynomial is irreducible on $\mathbb{Q}$

Prove: If $f,g \in \Bbb Z[x]$ then $C(fg) = C(f)C(g)$

Decompose in irreducible factors over $\mathbb{Z}_3[X]$

Degree of a polynomial zero over the simple extension attained by adjoining another zero.

If I erase one of the variables in an irreducible homogeneous polynomial, it's still irreducible

Show that $K(\sqrt{2\sqrt{2}-1})$ is a degree $4$ Abelian extension of $K=\Bbb Q (i\sqrt{14})$

Let $n\in\Bbb Z$ and let $f(x)=x^3-nx^2-(n+3)x-1$. Show that $f(x)$ is irreducible in $\Bbb Q[x]$.

The degree and minimal polynomial over $\mathbb{Q}$ of $j\sqrt{2}$

Study the irreducible of polynomial $P(X) = X^n + X + p$, with $p$ be a prime number and $n$ an integer $\geq 2$.

Power Series where partial sums are irreducible polynomials?

Irreducible polynomial divisible by all primes

The irreducibility of $X^3-X^2+1$ over $\mathbb{F}_9[X]$

If $p$ is irreducible, is $p(x^2)$ irreducible?

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