List questions from irreducible-polynomials

Published on 01 Mar 2015 - 4:22

599

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Finding primes such that a given polynomial is irreducible modulo $p$

Published on 03 Mar 2015 - 16:36

687

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How to prove that $x^9-9x^7+27x^5-30x^3+9x-1$ is irreducible in $\mathbb{Q}[x]$?

Published on 04 Mar 2015 - 8:37

217

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The polynomial $(X^2+2)^n+5(X^{2n-1}+10X^n+5)$ is irreducible in $\mathbb Z[X]$

Published on 04 Mar 2015 - 15:44

103

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How to go about proving that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$?

Published on 29 Mar 2026 - 4:26

325

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Complex roots of irreducible cubic in $\mathbb{Q}[x]$

Published on 28 Mar 2026 - 13:28

288

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Why doesn't there exist a ring homomorphism between these two rings?

Published on 08 Mar 2015 - 16:57

266

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Irreducibility of $1+x+\dots+x^{n-1}$ over $\mathbb{F}_2[x]$

Published on 13 Mar 2015 - 15:30

62

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The irreducibility of polynomials for specific cases

Published on 15 Mar 2015 - 17:33

1k

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Irreducible polynomial in $\mathbb Q[x]$ of degree $n$ having exactly $n-2$ real roots.

Published on 18 Mar 2015 - 2:57

149

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Polynomial in $\mathbb Q[x]$ with exactly 2 complex roots

Published on 18 Mar 2015 - 8:38

56

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Show that a polynomial $f(x)$ over a field $k$ is irreducible if the polynomial $f(x+1)$ is irreducible

Published on 19 Mar 2015 - 18:50

187

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Is $x^4 -4x^3+6x^2-4x-8$ irreducible over $\mathbb{Q}$?

Published on 19 Mar 2015 - 21:02

53

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Irreducibility of polynomials of a certain kind

Published on 20 Mar 2015 - 20:59

2.5k

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Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$

Published on 20 Mar 2015 - 21:53

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Subfields of $F_2[x] / (x^3 + x + 1)$

Finding primes such that a given polynomial is irreducible modulo $p$

How to prove that $x^9-9x^7+27x^5-30x^3+9x-1$ is irreducible in $\mathbb{Q}[x]$?

The polynomial $(X^2+2)^n+5(X^{2n-1}+10X^n+5)$ is irreducible in $\mathbb Z[X]$

How to go about proving that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$?

Complex roots of irreducible cubic in $\mathbb{Q}[x]$

Why doesn't there exist a ring homomorphism between these two rings?

Irreducibility of $1+x+\dots+x^{n-1}$ over $\mathbb{F}_2[x]$

The irreducibility of polynomials for specific cases

Irreducible polynomial in $\mathbb Q[x]$ of degree $n$ having exactly $n-2$ real roots.

Polynomial in $\mathbb Q[x]$ with exactly 2 complex roots

Show that a polynomial $f(x)$ over a field $k$ is irreducible if the polynomial $f(x+1)$ is irreducible

Is $x^4 -4x^3+6x^2-4x-8$ irreducible over $\mathbb{Q}$?

Irreducibility of polynomials of a certain kind

Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$

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