Question

Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

score 117 · Answer 1 · 2026-03-25 12:27:05

117

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Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Published on 25 Mar 2026 - 12:27

score 861 · Answer 2 · 2019-05-17 00:59:21

861

Views

Show that $x^2 +1$ is irreducible in $\mathbb{R}[x]$, but it has roots in $\mathbb{R}[x]\space/\space(x^2 +1) \cong \mathbb{C}$

Published on 17 May 2019 - 0:59

score 135 · Answer 3 · 2026-03-26 14:34:33

135

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Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Published on 26 Mar 2026 - 14:34

score 102 · Answer 4 · 2019-05-18 17:22:02

102

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Degree 2 Recurring monic polynomials

Published on 18 May 2019 - 17:22

score 155 · Answer 5 · 2019-05-19 19:02:59

155

Views

$f$ being irreducible over $\mathbb{Z}_{p}$ implies all equivalent polynomials of $f$ in $\mathbb{Z}[x]$ will be irreducible over $\mathbb{Z}$

Published on 19 May 2019 - 19:02

score 103 · Answer 6 · 2019-05-19 21:34:39

103

Views

Set of roots Hermite polynomials(probabilistic type)

Published on 19 May 2019 - 21:34

score 805 · Answer 7 · 2019-05-22 07:58:15

805

Views

If $p(x)$ is the minimal polynomial of $\alpha$, and $f(x) \in F[x]$, $f(\alpha) = 0$, Then $p(x) | f(x)$

Published on 22 May 2019 - 7:58

score 109 · Answer 8 · 2026-03-25 07:18:06

109

Views

Why does $f(x_n)\rightarrow 0$ imply that a subsequence converges to zero of $f$?

Published on 25 Mar 2026 - 7:18

score 35 · Answer 9 · 2019-05-25 08:17:07

35

Views

The polynomial $aX^2+bX+c$ of degree $2$ in a field $K$ with char$(K)\neq 2$ is irreducible if and only if $b^2-4ac$ is not a square in $K$.

Published on 25 May 2019 - 8:17

score 101 · Answer 10 · 2019-05-25 15:56:26

101

Views

Irreducibility of $x^n-a^n$ on $F(a^n)$ where $a$ is transcendental on $F$

Published on 25 May 2019 - 15:56

score 535 · Answer 11 · 2019-05-26 06:12:42

535

Views

Is there any degree 6 irreducible polynomial in $\Bbb Q[x]$ whose Galois group is $A_4$?

Published on 26 May 2019 - 6:12

score 187 · Answer 12 · 2019-05-30 12:32:31

187

Views

Find roots of primitive polynomial $x^2+4x+2$ in $\mathbb{Z}_{11}/(x^2+x+8)$

Published on 30 May 2019 - 12:32

score 125 · Answer 13 · 2019-06-04 17:20:49

125

Views

A field extension, the larger field is algebraically closed, are there finite subextensions of arbitrary large degree?

Published on 04 Jun 2019 - 17:20

score 54 · Answer 14 · 2019-06-06 15:24:33

54

Views

Let $E$ be an algebraic extension of $k$.

Published on 06 Jun 2019 - 15:24

score 52 · Answer 15 · 2019-06-06 20:30:05

52

Views

The polynomial $X-2Y$ in $\Bbb Z_{13}[X,Y]$ is irredicible

Published on 06 Jun 2019 - 20:30

List Question

Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Show that $x^2 +1$ is irreducible in $\mathbb{R}[x]$, but it has roots in $\mathbb{R}[x]\space/\space(x^2 +1) \cong \mathbb{C}$

Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Degree 2 Recurring monic polynomials

$f$ being irreducible over $\mathbb{Z}_{p}$ implies all equivalent polynomials of $f$ in $\mathbb{Z}[x]$ will be irreducible over $\mathbb{Z}$

Set of roots Hermite polynomials(probabilistic type)

If $p(x)$ is the minimal polynomial of $\alpha$, and $f(x) \in F[x]$, $f(\alpha) = 0$, Then $p(x) | f(x)$

Why does $f(x_n)\rightarrow 0$ imply that a subsequence converges to zero of $f$?

The polynomial $aX^2+bX+c$ of degree $2$ in a field $K$ with char$(K)\neq 2$ is irreducible if and only if $b^2-4ac$ is not a square in $K$.

Irreducibility of $x^n-a^n$ on $F(a^n)$ where $a$ is transcendental on $F$

Is there any degree 6 irreducible polynomial in $\Bbb Q[x]$ whose Galois group is $A_4$?

Find roots of primitive polynomial $x^2+4x+2$ in $\mathbb{Z}_{11}/(x^2+x+8)$

A field extension, the larger field is algebraically closed, are there finite subextensions of arbitrary large degree?

Let $E$ be an algebraic extension of $k$.

The polynomial $X-2Y$ in $\Bbb Z_{13}[X,Y]$ is irredicible

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