List questions from irreducible-polynomials

Published on 18 Jan 2016 - 16:23

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How can I get a irreducible polynomial of degree 8 over $Z_2[X]$?

Published on 18 Jan 2016 - 18:11

41

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Stuck with the statement: $t^4+2$ in $\mathbb{Z}_5$ gives rise to...

Published on 18 Jan 2016 - 22:52

567

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What is meant by "maximal proper factors" of a integer?

Published on 19 Jan 2016 - 12:22

967

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Show that $x^5-x^2+1$ is irreducible in $\mathbb{Q}[x]$.

Published on 20 Jan 2016 - 1:16

167

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Why is $x^3 + 3x + 2$ irreducible by plugging in elements of $\mathbb{Z}_5$

Published on 20 Jan 2016 - 2:12

118

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Irreducible polynomials and Eisenstein's criterion.

Published on 21 Jan 2016 - 13:50

512

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State whether $x^5-5x^4+10x^3-7x^2+8x-4$ is irreducible or not

Published on 21 Jan 2016 - 16:58

2k

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Prove $x^n+1$ is irreducible over $\mathbb{Q}[X]$ iff $n=2^k$ for $k \in \mathbb{N}$

Published on 21 Jan 2016 - 18:03

72

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How to separate a real integer polynomial into two with real/complex roots?

Published on 26 Jan 2016 - 6:15

2k

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Multiplicative Inverse in a $256$ Galois Field

Published on 26 Jan 2016 - 21:23

89

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Proof of equality of $2$ polynomials without using Galois Theory?

Published on 28 Mar 2026 - 5:22

120

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Simplifying Rational Expressions in a Finite Field Extension

Published on 30 Jan 2016 - 15:55

343

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List all elements of $\mathbb{Z}_5[x]/\langle x^2+3x+1\rangle$

Published on 31 Jan 2016 - 23:40

80

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On analogy between $\Bbb Z$ and $\Bbb F_q[x]$

Published on 23 Feb 2026 - 13:44

List Question

Difference between irreducible factors in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$

How can I get a irreducible polynomial of degree 8 over $Z_2[X]$?

Stuck with the statement: $t^4+2$ in $\mathbb{Z}_5$ gives rise to...

What is meant by "maximal proper factors" of a integer?

Show that $x^5-x^2+1$ is irreducible in $\mathbb{Q}[x]$.

Why is $x^3 + 3x + 2$ irreducible by plugging in elements of $\mathbb{Z}_5$

Irreducible polynomials and Eisenstein's criterion.

State whether $x^5-5x^4+10x^3-7x^2+8x-4$ is irreducible or not

Prove $x^n+1$ is irreducible over $\mathbb{Q}[X]$ iff $n=2^k$ for $k \in \mathbb{N}$

How to separate a real integer polynomial into two with real/complex roots?

Multiplicative Inverse in a $256$ Galois Field

Proof of equality of $2$ polynomials without using Galois Theory?

Simplifying Rational Expressions in a Finite Field Extension

List all elements of $\mathbb{Z}_5[x]/\langle x^2+3x+1\rangle$

On analogy between $\Bbb Z$ and $\Bbb F_q[x]$

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