List questions from irreducible-polynomials

Published on 14 May 2014 - 7:29

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Help to understand this polynomial trick

Published on 14 May 2014 - 18:33

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Prove a polynomial is irreducible over $\mathbb Q$

Published on 16 May 2014 - 21:24

70

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Let $f(x)\in F[x]$ ($F$ a field) be irreducible and let $\alpha$ be a root of $f(x)$. Then $h(x)\in(f(x))\Leftrightarrow h(\alpha)=0$?

Published on 18 May 2014 - 4:40

137

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Showing a polynomial is irreducible

Published on 18 May 2014 - 10:33

240

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Irreducibility of $1+X+\ldots+X^{p-1}$ over $\mathbb{Q}$

Published on 19 May 2014 - 17:36

5.1k

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Show that the polynomial $x^2 + x + 1$ is irreducible in $\mathbb Z/2\mathbb Z[x]$

Published on 20 May 2014 - 6:22

285

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Checking if a monic polynomial can be decomposed into linear factors

Published on 21 May 2014 - 18:13

544

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Degrees of factors of polynomial $f(x)=x^q-(ax^2+bx+c)\in \mathbb{F}_q[x]$

Published on 22 May 2014 - 2:39

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Galois Group of a cubic polynomial

Published on 23 May 2014 - 11:09

82

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Polynomials in $\Bbb Q[x]$ with same real root dont have common divisor with degree more than 1

Published on 25 May 2014 - 20:03

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$x^p-x+a$ irreducible for nonzero $a\in K$ a field of characteristic $p$ prime

Published on 25 Mar 2026 - 10:35

84

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Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

Published on 27 May 2014 - 18:35

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Polynomial irreducible - maximal ideal

Published on 31 May 2014 - 20:28

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$\gcd(f,f')=1$ Does this imply that f has not multiply irreducible factors in $\mathbb{C}[x]$?

Published on 01 Jun 2014 - 8:36

List Question

Krull dimension of a quotient ring

Help to understand this polynomial trick

Prove a polynomial is irreducible over $\mathbb Q$

Let $f(x)\in F[x]$ ($F$ a field) be irreducible and let $\alpha$ be a root of $f(x)$. Then $h(x)\in(f(x))\Leftrightarrow h(\alpha)=0$?

Showing a polynomial is irreducible

Irreducibility of $1+X+\ldots+X^{p-1}$ over $\mathbb{Q}$

Show that the polynomial $x^2 + x + 1$ is irreducible in $\mathbb Z/2\mathbb Z[x]$

Checking if a monic polynomial can be decomposed into linear factors

Degrees of factors of polynomial $f(x)=x^q-(ax^2+bx+c)\in \mathbb{F}_q[x]$

Galois Group of a cubic polynomial

Polynomials in $\Bbb Q[x]$ with same real root dont have common divisor with degree more than 1

$x^p-x+a$ irreducible for nonzero $a\in K$ a field of characteristic $p$ prime

Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

Polynomial irreducible - maximal ideal

$\gcd(f,f')=1$ Does this imply that f has not multiply irreducible factors in $\mathbb{C}[x]$?

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