Question

Irreducibility testing for integral cubic polynomials

score 64 · Answer 1 · 2026-04-01 21:27:39

64

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Irreducibility testing for integral cubic polynomials

Published on 01 Apr 2026 - 21:27

score 117 · Answer 2 · 2026-04-10 21:39:08

117

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Remainder in long division of a high degree polynomial by a quadratic polynomial

Published on 10 Apr 2026 - 21:39

score 150 · Answer 3 · 2021-07-10 07:53:10

150

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Is the polynomial $x^5 - 5x^4 + 7x^3 + x^2 + x - 1$ irreducible in $\mathbb{Z} [x]$ or in $\mathbb{Q} [x]$?

Published on 10 Jul 2021 - 7:53

score 361 · Answer 4 · 2021-07-11 03:13:37

361

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Is $\mathbb{F}_{2011^2}[x]/(x^4-6x-12)$ a field?

Published on 11 Jul 2021 - 3:13

score 51 · Answer 5 · 2026-03-26 11:17:36

51

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Can an irreducible polynomial over $\mathbb{F}_{q}[T]$ have multiple roots?

Published on 26 Mar 2026 - 11:17

score 48 · Answer 6 · 2021-07-12 19:10:01

48

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Show that if $F(x,y,z)$ is an irreducible homogenous polynomial over $\mathbb{C}$, then $F(1,y,z)$ is also irreducible over $\mathbb{C}$.

Published on 12 Jul 2021 - 19:10

score 54 · Answer 7 · 2026-04-11 16:49:34

54

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Determining the distinct conjugacy classes by obtaining Rational Cannonical forms using minimal polynomial

Published on 11 Apr 2026 - 16:49

score 65 · Answer 8 · 2021-07-15 11:27:57

65

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Irreducibility of $g(y)=y^n+qy+q^2$ in $\mathbb{Q}[y]$

Published on 15 Jul 2021 - 11:27

score 182 · Answer 9 · 2026-04-13 02:23:48

182

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Irreducible polynomial over normal extension

Published on 13 Apr 2026 - 2:23

score 134 · Answer 10 · 2021-07-20 06:52:41

134

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For any $ a \in \mathbb{N}$ ; $f(x)=x^4+(4a+2)x^2+1$ is irreducible in $\mathbb{Z}[X]$ & reducible mod $p$ for all $p$.

Published on 20 Jul 2021 - 6:52

score 81 · Answer 11 · 2026-03-30 12:24:19

81

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is $f(x) = 20x^5-35x^4+10x^3-1$ irreducible over $\Bbb Q [\sqrt{3}]$?

Published on 30 Mar 2026 - 12:24

score 56 · Answer 12 · 2021-07-21 19:58:08

56

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Let $K=F(\frac{x^7}{x^5+x^3+3x+1})$, where $F$ is a field. Determine $[F(x): K]$.

Published on 21 Jul 2021 - 19:58

score 36 · Answer 13 · 2026-04-12 16:22:00

36

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Meaning of irreducible polynomial that is factor of $P$

Published on 12 Apr 2026 - 16:22

score 116 · Answer 14 · 2021-07-22 08:36:22

116

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Generalization of Murty's Irreducibility Criterion

Published on 22 Jul 2021 - 8:36

score 84 · Answer 15 · 2026-03-27 20:12:59

84

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Proving this polynomial is irreducible

Published on 27 Mar 2026 - 20:12

List Question

Irreducibility testing for integral cubic polynomials

Remainder in long division of a high degree polynomial by a quadratic polynomial

Is the polynomial $x^5 - 5x^4 + 7x^3 + x^2 + x - 1$ irreducible in $\mathbb{Z} [x]$ or in $\mathbb{Q} [x]$?

Is $\mathbb{F}_{2011^2}[x]/(x^4-6x-12)$ a field?

Can an irreducible polynomial over $\mathbb{F}_{q}[T]$ have multiple roots?

Show that if $F(x,y,z)$ is an irreducible homogenous polynomial over $\mathbb{C}$, then $F(1,y,z)$ is also irreducible over $\mathbb{C}$.

Determining the distinct conjugacy classes by obtaining Rational Cannonical forms using minimal polynomial

Irreducibility of $g(y)=y^n+qy+q^2$ in $\mathbb{Q}[y]$

Irreducible polynomial over normal extension

For any $ a \in \mathbb{N}$ ; $f(x)=x^4+(4a+2)x^2+1$ is irreducible in $\mathbb{Z}[X]$ & reducible mod $p$ for all $p$.

is $f(x) = 20x^5-35x^4+10x^3-1$ irreducible over $\Bbb Q [\sqrt{3}]$?

Let $K=F(\frac{x^7}{x^5+x^3+3x+1})$, where $F$ is a field. Determine $[F(x): K]$.

Meaning of irreducible polynomial that is factor of $P$

Generalization of Murty's Irreducibility Criterion

Proving this polynomial is irreducible

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