List questions from irreducible-polynomials

Published on 13 Apr 2026 - 0:19

81

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What is the highest value of $n$ be to reduce a general polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0=0$ to $y^n+py+q=0 ?$

Published on 12 Apr 2026 - 22:41

242

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Prove that the polynomial $x^4 -5x^2+x+1$ is irreducible over the ring $\mathbb{Z}[x]$.

Published on 15 Apr 2026 - 5:32

68

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Show that $X^n-p$, for p prime, is irreducible.

Published on 13 Apr 2026 - 20:37

273

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Is $x^4+22x^2+1$ irreducible over $\mathbb{Q}$?

Published on 15 Apr 2026 - 7:53

107

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How to prove that $(x^{p^2}-1)/(x^{p}-1)$ is irreducible over $\mathbb{Q}$ if $p$ is prime?

Published on 15 Apr 2026 - 4:07

89

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Find a polynomial $f \in \mathbb{Q}[x]$ with $f(x)=\frac{1}{x}$

Published on 02 Apr 2026 - 23:40

62

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Irreducibility of polynomial P(X) = X

Published on 14 Apr 2026 - 12:11

186

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Show that $3x^5-4x^3-6x^2+6$ is irreducible over $\mathbb{Q}[x]$

Published on 15 Dec 2022 - 1:22

69

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Question about how to use Eisenstein's criterion

Published on 12 Apr 2026 - 21:32

112

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Show: $f=x^p - \alpha$ irreducible and inseparable in field $F(\alpha)$, where $charF=p>0$ and $\alpha$ transcendental over F

Published on 14 Apr 2026 - 17:57

89

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Is $4x+2$ irreducible over $\Bbb{Q}[x]$ and over $\Bbb{Z}[x]$

Published on 15 Apr 2026 - 9:24

124

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Can all the roots of $ax^5+bx^2+c=0$, with real coefficients and $a,c\neq0$, be real numbers?

Published on 11 Apr 2026 - 15:00

54

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identity of P(X) = P(X-nq) if P(X) has roots in C but is irreducible in Q

Published on 15 Apr 2026 - 8:10

71

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Irreductibility of $x^p-t$ for fields $F$ with characteristic $p$ and such that $t$ has not a $p$-root in $F$

Published on 12 Apr 2026 - 8:28

List Question

Prime Ideals in Polynomial Quotient Ring

What is the highest value of $n$ be to reduce a general polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0=0$ to $y^n+py+q=0 ?$

Prove that the polynomial $x^4 -5x^2+x+1$ is irreducible over the ring $\mathbb{Z}[x]$.

Show that $X^n-p$, for p prime, is irreducible.

Is $x^4+22x^2+1$ irreducible over $\mathbb{Q}$?

How to prove that $(x^{p^2}-1)/(x^{p}-1)$ is irreducible over $\mathbb{Q}$ if $p$ is prime?

Find a polynomial $f \in \mathbb{Q}[x]$ with $f(x)=\frac{1}{x}$

Irreducibility of polynomial P(X) = X

Show that $3x^5-4x^3-6x^2+6$ is irreducible over $\mathbb{Q}[x]$

Question about how to use Eisenstein's criterion

Show: $f=x^p - \alpha$ irreducible and inseparable in field $F(\alpha)$, where $charF=p>0$ and $\alpha$ transcendental over F

Is $4x+2$ irreducible over $\Bbb{Q}[x]$ and over $\Bbb{Z}[x]$

Can all the roots of $ax^5+bx^2+c=0$, with real coefficients and $a,c\neq0$, be real numbers?

identity of P(X) = P(X-nq) if P(X) has roots in C but is irreducible in Q

Irreductibility of $x^p-t$ for fields $F$ with characteristic $p$ and such that $t$ has not a $p$-root in $F$

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