List questions from irreducible-polynomials

Published on 13 Jan 2021 - 11:08

60

Views

Investigate if the following polynomial in Q [x] is reducible or irreducible: $x^5+x+1$

Published on 13 Jan 2021 - 11:30

137

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Investigate if the following polynomial in Q[x] is reducible or irreducible: $x^3-5x^2+2x+1$

Published on 13 Jan 2021 - 12:39

93

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Showing that $x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$ [Direct approach].

Published on 13 Jan 2021 - 22:44

19

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Show that a polynomial is inside $\Bbb Q^*$

Published on 15 Jan 2021 - 13:29

64

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What happens if $f(x)$ is irreducible but $f(g(x))$ is reducible?

Published on 20 Jan 2021 - 13:30

115

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Factoring a multivariate polynomial.

Published on 12 Apr 2026 - 2:54

31

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Controlling the discriminant size of a polynomial using roots

Published on 26 Mar 2026 - 7:33

74

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Rabin's test for irreducibility of deg 3 poly in $\mathbb F_{3}[X]$

Published on 08 Apr 2026 - 2:33

162

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Prove $g(x)$ is irreducible over $F$.

Published on 23 Jan 2021 - 0:55

29

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Factorize certain polynomials as product of irreducibles

Published on 12 Apr 2026 - 0:50

60

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Are polynomials with more terms less likely to be reducible?

Published on 12 Apr 2026 - 6:55

337

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$x^2+y^n-1$ is absolutely irreducible

Published on 27 Jan 2021 - 9:33

196

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$f(x)$ is irreducible over $\Bbb Z$ if and only if it is irreducible over $\Bbb Q$.

Published on 27 Jan 2021 - 15:38

178

Views

Proving $x^{nm}-c$ irreducible $\leftrightarrow x^n-c,x^m-c$ irreducible

Published on 27 Jan 2021 - 18:43

List Question

"smallest" irreducible polynomial over GF(p)

Investigate if the following polynomial in Q [x] is reducible or irreducible: $x^5+x+1$

Investigate if the following polynomial in Q[x] is reducible or irreducible: $x^3-5x^2+2x+1$

Showing that $x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$ [Direct approach].

Show that a polynomial is inside $\Bbb Q^*$

What happens if $f(x)$ is irreducible but $f(g(x))$ is reducible?

Factoring a multivariate polynomial.

Controlling the discriminant size of a polynomial using roots

Rabin's test for irreducibility of deg 3 poly in $\mathbb F_{3}[X]$

Prove $g(x)$ is irreducible over $F$.

Factorize certain polynomials as product of irreducibles

Are polynomials with more terms less likely to be reducible?

$x^2+y^n-1$ is absolutely irreducible

$f(x)$ is irreducible over $\Bbb Z$ if and only if it is irreducible over $\Bbb Q$.

Proving $x^{nm}-c$ irreducible $\leftrightarrow x^n-c,x^m-c$ irreducible

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