Question

Prove all roots of $p_n(x)-x$ are real and distinct

score 302 · Answer 1 · 2026-04-01 23:14:41

302

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Prove all roots of $p_n(x)-x$ are real and distinct

Published on 01 Apr 2026 - 23:14

score 104 · Answer 2 · 2026-03-26 12:08:28

104

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Why is $(x^{2n+1} - (2n+1)x^{n+1} + (2n+1)x^n - 1)/(x-1)^3$ irreducible?

Published on 26 Mar 2026 - 12:08

score 39 · Answer 3 · 2026-04-11 08:19:05

39

Views

Differences between factoring an equation and dividing one

Published on 11 Apr 2026 - 8:19

score 239 · Answer 4 · 2026-04-02 01:00:28

239

Views

Finding remainder when unknown $f(x)$ is divided to $g(x)$

Published on 02 Apr 2026 - 1:00

score 135 · Answer 5 · 2019-01-20 09:57:31

135

Views

Is there a trick to solve $\int_{-1}^1 \frac{P(t)}{\sqrt{1-t^2}}{\rm d}t=a[P(x_1)+P(x_2)+P(x_3)]$?

Published on 20 Jan 2019 - 9:57

score 119 · Answer 6 · 2026-04-05 12:00:13

119

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Finding all roots of $x^6 + 2 x^5 + 2 x^4 + 3 x^2 + 6 x + 6$, knowing that one root is $x=-1+i$.

Published on 05 Apr 2026 - 12:00

score 1.6k · Answer 7 · 2026-03-26 12:06:45

1.6k

Views

Silly question: are polynomials "X" and "X^2" reducible?

Published on 26 Mar 2026 - 12:06

score 70 · Answer 8 · 2026-04-11 15:56:10

70

Views

Tricky problem of infinite harmonic sum of polynomials

Published on 11 Apr 2026 - 15:56

score 246 · Answer 9 · 2026-03-26 02:53:48

246

Views

How to compute the syndrome polynomial? BCH code

Published on 26 Mar 2026 - 2:53

score 53 · Answer 10 · 2026-03-28 00:48:01

53

Views

Prove that each element of polynomial ring with irreducible characteristic has exactly one minimum polynomial.

Published on 28 Mar 2026 - 0:48

score 197 · Answer 11 · 2026-04-09 23:05:11

197

Views

Does a linear change of coordinate affect the ireducibility of a polynomial?

Published on 09 Apr 2026 - 23:05

score 46 · Answer 12 · 2026-04-04 09:34:42

46

Views

Certain algebraic dependence of two polynomials

Published on 04 Apr 2026 - 9:34

score 122 · Answer 13 · 2026-04-10 22:58:10

122

Views

Show a polynomial of degree 4 in 7 variables is positive

Published on 10 Apr 2026 - 22:58

score 41 · Answer 14 · 2026-04-11 04:03:08

41

Views

Root dependence on coefficient terms

Published on 11 Apr 2026 - 4:03

score 79 · Answer 15 · 2026-04-11 14:30:06

79

Views

Divisibility of a certain two variable polynomial by $x$

Published on 11 Apr 2026 - 14:30

List Question

Prove all roots of $p_n(x)-x$ are real and distinct

Why is $(x^{2n+1} - (2n+1)x^{n+1} + (2n+1)x^n - 1)/(x-1)^3$ irreducible?

Differences between factoring an equation and dividing one

Finding remainder when unknown $f(x)$ is divided to $g(x)$

Is there a trick to solve $\int_{-1}^1 \frac{P(t)}{\sqrt{1-t^2}}{\rm d}t=a[P(x_1)+P(x_2)+P(x_3)]$?

Finding all roots of $x^6 + 2 x^5 + 2 x^4 + 3 x^2 + 6 x + 6$, knowing that one root is $x=-1+i$.

Silly question: are polynomials "X" and "X^2" reducible?

Tricky problem of infinite harmonic sum of polynomials

How to compute the syndrome polynomial? BCH code

Prove that each element of polynomial ring with irreducible characteristic has exactly one minimum polynomial.

Does a linear change of coordinate affect the ireducibility of a polynomial?

Certain algebraic dependence of two polynomials

Show a polynomial of degree 4 in 7 variables is positive

Root dependence on coefficient terms

Divisibility of a certain two variable polynomial by $x$

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