List questions from irreducible-polynomials

Published on 23 Apr 2015 - 9:08

4.7k

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Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$

Published on 24 Apr 2015 - 16:56

148

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Show that $x^{8}+x^{4}+x^{3}+x+1$ is irreducible over $\mathbb{Z}_{2}[x]$

Published on 26 Apr 2015 - 5:37

592

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"p-adic absolute value" in polynomial ring

Published on 31 Mar 2026 - 20:03

329

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Minimal polynomial of $\sqrt[3]{2} + \omega$ over $\mathbb{Q}.$

Published on 27 Apr 2015 - 20:19

630

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Irreducibility of $x^{2n}+x^n+1$

Published on 27 Apr 2015 - 22:17

888

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Show that $P = (f(x))$ is a maximal ideal of $F(x)$

Published on 03 Apr 2026 - 3:19

69

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Long division for multipolynomial expression, little o notation

Published on 02 Apr 2026 - 3:54

1.4k

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Irreducibility of polynomials over finite field of integers $\bmod 11$.

Published on 28 Apr 2015 - 10:17

2.9k

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$x^p -x-c$ is irreducible over a field of characteristic $p$ if it has no root in the field

Published on 28 Apr 2015 - 16:11

911

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How can I prove the polynomial f is irreducible

Published on 29 Apr 2015 - 18:03

3.7k

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Prove that $f=x^4-4x^2+16\in\mathbb{Q}[x]$ is irreducible

Published on 01 May 2015 - 15:15

1k

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Irreducible polynomial over a field $k$ with $char\ k = p > 0$

Published on 27 Mar 2026 - 20:31

961

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Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.

Published on 02 May 2015 - 21:52

320

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Checking irreducibility of a polynomial over a finite field

Published on 30 Mar 2026 - 5:32

List Question

How do we determine the decomposition of $p\mathcal{O}_K$ in $K = \mathbb{Q}(\sqrt[3]{5})$?

Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$

Show that $x^{8}+x^{4}+x^{3}+x+1$ is irreducible over $\mathbb{Z}_{2}[x]$

"p-adic absolute value" in polynomial ring

Minimal polynomial of $\sqrt[3]{2} + \omega$ over $\mathbb{Q}.$

Irreducibility of $x^{2n}+x^n+1$

Show that $P = (f(x))$ is a maximal ideal of $F(x)$

Long division for multipolynomial expression, little o notation

Irreducibility of polynomials over finite field of integers $\bmod 11$.

$x^p -x-c$ is irreducible over a field of characteristic $p$ if it has no root in the field

How can I prove the polynomial f is irreducible

Prove that $f=x^4-4x^2+16\in\mathbb{Q}[x]$ is irreducible

Irreducible polynomial over a field $k$ with $char\ k = p > 0$

Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.

Checking irreducibility of a polynomial over a finite field

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