Question

Prove The Derivative Rules in the Ring of Polynomials. How to show Leibniz's rule?

score 1.2k · Answer 1 · 2026-04-12 03:14:49

1.2k

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Prove The Derivative Rules in the Ring of Polynomials. How to show Leibniz's rule?

Published on 12 Apr 2026 - 3:14

score 40 · Answer 2 · 2026-04-15 21:54:48

40

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$f(x)=(x-a)(x-a_2)...(x-a_n)\in F[x]$ where $F$ is a field and $a_j\in $ for $j=1,2,...,n$ has no repeated roots iff gcd$(f(x),f'(x))=1\in F[x]$

Published on 15 Apr 2026 - 21:54

score 89 · Answer 3 · 2026-04-14 20:13:38

89

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Find the value of $\alpha^{\frac13}+\beta^{\frac13}$

Published on 14 Apr 2026 - 20:13

score 592 · Answer 4 · 2026-04-17 09:55:35

592

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real solution of equation $(x^2+6x+7)^2+6(x^2+6x+7)+7=x$ is

Published on 17 Apr 2026 - 9:55

score 493 · Answer 5 · 2026-04-13 15:34:10

493

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Non-isomorphic graphs with same Tutte polynomial

Published on 13 Apr 2026 - 15:34

score 52 · Answer 6 · 2026-04-14 08:03:16

52

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For complex polynomial $f(z)$ show there are finitely many $w$ such that $f(v) = w \neq v$ implies $f'(v) =0$.

Published on 14 Apr 2026 - 8:03

score 279 · Answer 7 · 2026-04-16 15:32:14

279

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Show that any complex polynomial of degree $n \ge 2$ has finitely many neutral or attracting orbits

Published on 16 Apr 2026 - 15:32

score 90 · Answer 8 · 2026-04-15 15:43:10

90

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If $F\subseteq K$ are fields, $\alpha \in K$ Prove $\alpha$ is algebraic over $F$

Published on 15 Apr 2026 - 15:43

score 100 · Answer 9 · 2026-04-15 17:38:33

100

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Show that $\frac{x(x-1) \dots (x-n+1)}{n!} \in \mathbb{Z}$ with $x \in \mathbb{Z}$

Published on 15 Apr 2026 - 17:38

score 252 · Answer 10 · 2026-04-17 15:48:44

252

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Long division of $\frac{3x^3-x^2-13x-13}{x^2-x-6}$

Published on 17 Apr 2026 - 15:48

score 46 · Answer 11 · 2026-04-16 14:47:12

46

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GCD of $f=X^3 +9X^2 +10X +3$ and $g= X^2 -X -2$ in $\mathbb{Z}/5\mathbb{Z}$.

Published on 16 Apr 2026 - 14:47

score 71 · Answer 12 · 2026-04-14 00:04:04

71

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Polynomials in the Pancake problem

Published on 14 Apr 2026 - 0:04

score 41 · Answer 13 · 2026-04-09 07:48:21

41

Views

Tough test polynomials for (finite precision) complex root finding methods, especially Aberth's method

Published on 09 Apr 2026 - 7:48

score 871 · Answer 14 · 2026-04-09 10:28:52

871

Views

Is it possible to graph complex zeros of a polynomial?

Published on 09 Apr 2026 - 10:28

score 137 · Answer 15 · 2026-04-14 16:16:23

137

Views

Irreducible polynomials for that each output is divisible by an integer n

Published on 14 Apr 2026 - 16:16

List Question

Prove The Derivative Rules in the Ring of Polynomials. How to show Leibniz's rule?

$f(x)=(x-a)(x-a_2)...(x-a_n)\in F[x]$ where $F$ is a field and $a_j\in $ for $j=1,2,...,n$ has no repeated roots iff gcd$(f(x),f'(x))=1\in F[x]$

Find the value of $\alpha^{\frac13}+\beta^{\frac13}$

real solution of equation $(x^2+6x+7)^2+6(x^2+6x+7)+7=x$ is

Non-isomorphic graphs with same Tutte polynomial

For complex polynomial $f(z)$ show there are finitely many $w$ such that $f(v) = w \neq v$ implies $f'(v) =0$.

Show that any complex polynomial of degree $n \ge 2$ has finitely many neutral or attracting orbits

If $F\subseteq K$ are fields, $\alpha \in K$ Prove $\alpha$ is algebraic over $F$

Show that $\frac{x(x-1) \dots (x-n+1)}{n!} \in \mathbb{Z}$ with $x \in \mathbb{Z}$

Long division of $\frac{3x^3-x^2-13x-13}{x^2-x-6}$

GCD of $f=X^3 +9X^2 +10X +3$ and $g= X^2 -X -2$ in $\mathbb{Z}/5\mathbb{Z}$.

Polynomials in the Pancake problem

Tough test polynomials for (finite precision) complex root finding methods, especially Aberth's method

Is it possible to graph complex zeros of a polynomial?

Irreducible polynomials for that each output is divisible by an integer n

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