Question

The irreducibility of $x^{16}-2x^8+8x+1$ over the rationals

score 254 · Answer 1 · 2022-08-12 09:19:13

254

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The irreducibility of $x^{16}-2x^8+8x+1$ over the rationals

Published on 12 Aug 2022 - 9:19

score 53 · Answer 2 · 2022-08-18 11:35:57

53

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Find the prime factorization of $x^3-x+1$ in $\Bbb Z_3[x]$ and in $\Bbb Z_5[x]$.

Published on 18 Aug 2022 - 11:35

score 135 · Answer 3 · 2022-08-24 00:32:42

135

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Irreducibility of polynomials in $\mathbb{F}_p[x][y]$

Published on 24 Aug 2022 - 0:32

score 221 · Answer 4 · 2026-04-13 19:35:26

221

Views

Help with a finite field exercise. How to find the minimal polynomial of a given root in a given field.

Published on 13 Apr 2026 - 19:35

score 31 · Answer 5 · 2026-04-13 15:02:20

31

Views

Given a finite field of primer order and a certain degree extension, how one finds the "best" irreducible polynomial in terms of computability?

Published on 13 Apr 2026 - 15:02

score 469 · Answer 6 · 2022-08-26 17:13:52

469

Views

An irreducible polynomial is inseparable iff the exponent of each irreducible factor over an algebraic closure is a multiple of the characteristic

Published on 26 Aug 2022 - 17:13

score 63 · Answer 7 · 2026-04-14 04:41:55

63

Views

Two polynomials have finitely many common roots

Published on 14 Apr 2026 - 4:41

score 177 · Answer 8 · 2022-08-28 13:51:50

177

Views

Show that $x^{12} - 18x^6 + 82$ is irreducible over $\mathbb{F}_p$

Published on 28 Aug 2022 - 13:51

score 47 · Answer 9 · 2026-04-14 19:00:41

47

Views

Find the number of elements for which polynomial is irreducible

Published on 14 Apr 2026 - 19:00

score 111 · Answer 10 · 2026-03-28 09:57:07

111

Views

$x^4+x^3+x^2+x+1$ is irreducible over $\mathbb{F}_2$

Published on 28 Mar 2026 - 9:57

score 144 · Answer 11 · 2022-09-04 13:44:10

144

Views

Is $f(X)=X^7+6X^5+5X^2+9$ irreducible over $\Bbb{Z}$?

Published on 04 Sep 2022 - 13:44

score 39 · Answer 12 · 2026-04-11 18:59:27

39

Views

Irreducibles in ring of polynomials

Published on 11 Apr 2026 - 18:59

score 141 · Answer 13 · 2022-09-13 01:29:08

141

Views

Factorize $x^6-2x^5-7x^4+8x^3+32x^2-64$

Published on 13 Sep 2022 - 1:29

score 431 · Answer 14 · 2022-09-15 11:10:16

431

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Solve in exact form: $x^6 - x^5 + 4 x^4 - 4 x^3 + 4 x^2 - x + 1=0$ ( WolframAlpha failed)

Published on 15 Sep 2022 - 11:10

score 360 · Answer 15 · 2022-09-15 15:49:26

360

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A precalculus solution for $x^6 - 3 x^4 + 2 x^3 + 3 x^2 - 3 x + 1 =0$

Published on 15 Sep 2022 - 15:49

List Question

The irreducibility of $x^{16}-2x^8+8x+1$ over the rationals

Find the prime factorization of $x^3-x+1$ in $\Bbb Z_3[x]$ and in $\Bbb Z_5[x]$.

Irreducibility of polynomials in $\mathbb{F}_p[x][y]$

Help with a finite field exercise. How to find the minimal polynomial of a given root in a given field.

Given a finite field of primer order and a certain degree extension, how one finds the "best" irreducible polynomial in terms of computability?

An irreducible polynomial is inseparable iff the exponent of each irreducible factor over an algebraic closure is a multiple of the characteristic

Two polynomials have finitely many common roots

Show that $x^{12} - 18x^6 + 82$ is irreducible over $\mathbb{F}_p$

Find the number of elements for which polynomial is irreducible

$x^4+x^3+x^2+x+1$ is irreducible over $\mathbb{F}_2$

Is $f(X)=X^7+6X^5+5X^2+9$ irreducible over $\Bbb{Z}$?

Irreducibles in ring of polynomials

Factorize $x^6-2x^5-7x^4+8x^3+32x^2-64$

Solve in exact form: $x^6 - x^5 + 4 x^4 - 4 x^3 + 4 x^2 - x + 1=0$ ( WolframAlpha failed)

A precalculus solution for $x^6 - 3 x^4 + 2 x^3 + 3 x^2 - 3 x + 1 =0$

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