List questions from polynomials

Published on 12 Apr 2026 - 14:03

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

Published on 17 Apr 2026 - 1:32

67

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At most two of the three polynomials $p(x)$, $p(x) - 1$, $p(x) - c$ are squares in $k[x]$

Published on 16 Apr 2026 - 14:30

172

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Prove that the only solution to $X^4+4=pY^4$. is $X=\pm 1,Y=\pm 1,p=5$ for $p \ge 3$ prime.

Published on 16 Apr 2026 - 2:46

21

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How to judge that a Boolean polynomial cannot be divisible by another?

Published on 10 Apr 2026 - 21:21

234

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How do you check if a polynomial system has solutions

Published on 09 Apr 2026 - 19:32

81

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Prove that there is no $a\in \mathbb R$ so that $f(x)= e^x(x^2+a) $ has only one extremum

Published on 15 Apr 2026 - 20:03

75

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How to approach this

Published on 10 Apr 2026 - 9:39

44

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searching for a matrix, which brings $f(x)$ to $f(x-1)$ for polynomials up to degree of $2$ and considering the basis $(1,x,x^2)$

Published on 16 Apr 2026 - 5:04

274

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Show that $x^n -1 \mid x^k -1 \Leftrightarrow n \mid k$

Published on 16 Apr 2026 - 5:11

105

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How to find $P(-2)$ here?

Published on 11 Apr 2026 - 5:58

1.5k

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Completing the square to find if quadratic form is positive definite.

Published on 25 Mar 2026 - 15:51

391

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Congruence in F[x], proof involving infinity

Published on 13 Apr 2026 - 18:35

51

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All coefficients of $P(x)$ are divisible by $7$

Published on 13 Apr 2026 - 12:54

210

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Find the degree of a field extension

Published on 15 Apr 2026 - 4:26

List Question

Polynomial division over an extension

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

At most two of the three polynomials $p(x)$, $p(x) - 1$, $p(x) - c$ are squares in $k[x]$

Prove that the only solution to $X^4+4=pY^4$. is $X=\pm 1,Y=\pm 1,p=5$ for $p \ge 3$ prime.

How to judge that a Boolean polynomial cannot be divisible by another?

How do you check if a polynomial system has solutions

Prove that there is no $a\in \mathbb R$ so that $f(x)= e^x(x^2+a) $ has only one extremum

How to approach this

searching for a matrix, which brings $f(x)$ to $f(x-1)$ for polynomials up to degree of $2$ and considering the basis $(1,x,x^2)$

Show that $x^n -1 \mid x^k -1 \Leftrightarrow n \mid k$

How to find $P(-2)$ here?

Completing the square to find if quadratic form is positive definite.

Congruence in F[x], proof involving infinity

All coefficients of $P(x)$ are divisible by $7$

Find the degree of a field extension

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