List questions from irreducible-polynomials

Published on 31 Dec 2015 - 16:57

151

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The irreducibility of $t^4 + 2$ over $\mathbb{Z}_5$

Published on 31 Dec 2015 - 21:54

126

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Alternating irreducibility of polynomial $t^n + t^{n-1} + \ldots + t + 1$?

Published on 01 Jan 2016 - 2:06

1.6k

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Every polynomial of odd degree $\ge 3$ over $\mathbb{R}[x]$ is reducible over $\mathbb{R}$

Published on 01 Jan 2016 - 17:35

879

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Cosets of $\mathbb{R}[x] / \langle x²+1 \rangle$

Published on 02 Jan 2016 - 1:04

112

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Cosets of $\mathbb{Z}_2[x]/<x²+1>$

Published on 02 Jan 2016 - 2:26

112

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Prove $p(x) = x^3+x+1\in\mathbb{Z}_5[x]$ is irreducible over $\mathbb{Z}_5$

Published on 02 Jan 2016 - 5:25

45

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Showing that $1$ is the only root in $f=x^5 -1 \in \mathbb{F}_p[x]$ if $p-1$ is not divisible by $5$

Published on 02 Jan 2016 - 12:06

115

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Decomposing $x^4-5x^2+6$ over some fields

Published on 02 Jan 2016 - 16:40

362

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How to factor $x^6+x^5-3\,x^4+2\,x^3+3\,x^2+x-1$ by hand?

Published on 02 Jan 2016 - 18:06

96

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Decomposing polynomials over $\mathbb{Z}_3$

Published on 02 Jan 2016 - 21:03

92

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Check if $X^3 -2$ is irreducible or not in $\mathbb{Z}_{31} [X]$

Published on 03 Jan 2016 - 18:20

359

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Show that $X^p-X-1\in \mathbb Q[X]$ is irreducible.

Published on 04 Jan 2016 - 20:19

88

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Which of the following field properties are correct?

Published on 05 Jan 2016 - 4:50

701

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If $f(x,y)\in R[x,y]$ is an irreducible polynomial, is $R[x,y]/f(x,y)$ a field?

Published on 07 Jan 2016 - 17:24

List Question

Factoring a polynomial which shares the same zeros as another

The irreducibility of $t^4 + 2$ over $\mathbb{Z}_5$

Alternating irreducibility of polynomial $t^n + t^{n-1} + \ldots + t + 1$?

Every polynomial of odd degree $\ge 3$ over $\mathbb{R}[x]$ is reducible over $\mathbb{R}$

Cosets of $\mathbb{R}[x] / \langle x²+1 \rangle$

Cosets of $\mathbb{Z}_2[x]/<x²+1>$

Prove $p(x) = x^3+x+1\in\mathbb{Z}_5[x]$ is irreducible over $\mathbb{Z}_5$

Showing that $1$ is the only root in $f=x^5 -1 \in \mathbb{F}_p[x]$ if $p-1$ is not divisible by $5$

Decomposing $x^4-5x^2+6$ over some fields

How to factor $x^6+x^5-3\,x^4+2\,x^3+3\,x^2+x-1$ by hand?

Decomposing polynomials over $\mathbb{Z}_3$

Check if $X^3 -2$ is irreducible or not in $\mathbb{Z}_{31} [X]$

Show that $X^p-X-1\in \mathbb Q[X]$ is irreducible.

Which of the following field properties are correct?

If $f(x,y)\in R[x,y]$ is an irreducible polynomial, is $R[x,y]/f(x,y)$ a field?

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