List questions from irreducible-polynomials

Published on 13 Apr 2026 - 18:56

40

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Showing a curve is not a variety using Bezout's theorem.

Published on 02 Apr 2026 - 14:19

40

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Prove $3^{rd}$ degree polynomial, $f \in \mathbb{F}[x]$ is irreducible in $\mathbb{F}[x]$ if it has no roots in $\mathbb{F}$

Published on 03 May 2022 - 21:15

144

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Show that $f \in \mathbb{Z}_{5}[x]$ is irreducible

Published on 13 Apr 2026 - 21:59

198

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Is $X^7 + X^4 + 1$ irreducible over $Q(X)$?

Published on 06 May 2022 - 6:46

185

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Finding subfields of an Extension Field

Published on 13 Apr 2026 - 17:30

53

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The Galois group of an irreducible quartic whose roots are pairwise rationally independent

Published on 13 Apr 2026 - 3:05

119

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Infinitely large Galois extensions of $\mathbb Q$ inside $\mathbb Q_p$

Published on 30 Mar 2026 - 17:08

563

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If $f(x)$ is irreducible, is $f(x^k)$ irreducible?

Published on 14 Apr 2026 - 10:40

86

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Show that $f(t)=t^8-2t^4+9$ is the minimal polynomial of $\alpha = \sqrt{i+\sqrt 2}$ over $\mathbb{Q}$

Published on 15 May 2022 - 15:09

313

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When is the polynomial $X^a+Y^b \in \mathbb{Q}[X,Y]$ irreducible?

Published on 16 May 2022 - 15:57

133

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How to expand $x(x-1)(x-2)...(x-k)$

Published on 18 May 2022 - 12:54

450

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find all irreducible polynomials of degree 2 and 3 over Z5

Published on 19 May 2022 - 19:15

63

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How to get a polynomial corresponding to a solvable Galois group of order 60?

Published on 12 Apr 2026 - 20:44

141

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$2ix^4 − 10x^3 + (4 − 2i)x + 8 + 6i$ irreducible in $\mathbb Z[i][x]$ and in $\mathbb Q[i][x]$

Published on 21 May 2022 - 16:00

List Question

Splitting field of $x^4+2$

Showing a curve is not a variety using Bezout's theorem.

Prove $3^{rd}$ degree polynomial, $f \in \mathbb{F}[x]$ is irreducible in $\mathbb{F}[x]$ if it has no roots in $\mathbb{F}$

Show that $f \in \mathbb{Z}_{5}[x]$ is irreducible

Is $X^7 + X^4 + 1$ irreducible over $Q(X)$?

Finding subfields of an Extension Field

The Galois group of an irreducible quartic whose roots are pairwise rationally independent

Infinitely large Galois extensions of $\mathbb Q$ inside $\mathbb Q_p$

If $f(x)$ is irreducible, is $f(x^k)$ irreducible?

Show that $f(t)=t^8-2t^4+9$ is the minimal polynomial of $\alpha = \sqrt{i+\sqrt 2}$ over $\mathbb{Q}$

When is the polynomial $X^a+Y^b \in \mathbb{Q}[X,Y]$ irreducible?

How to expand $x(x-1)(x-2)...(x-k)$

find all irreducible polynomials of degree 2 and 3 over Z5

How to get a polynomial corresponding to a solvable Galois group of order 60?

$2ix^4 − 10x^3 + (4 − 2i)x + 8 + 6i$ irreducible in $\mathbb Z[i][x]$ and in $\mathbb Q[i][x]$

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