List questions from extension-field

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Irreducible Polynomial Field Extensions with Root $\cos \frac{2\pi}{7}$

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How to prove irreducibility of this polynomial?

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Prove that $x^2 − 2$ is irreducible over $\mathbb Q (\sqrt 3)$

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Inverse of $2 − 3i \text{ in } \Bbb Q(i).$

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Inverse of $α∈Z_3(α)$ where $α^3+α^2+2=0$

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A proof needed in minimal polynomial.

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Prove that $F(x)/F(\frac{x^3}{x + 1})$ is simple algebraic extension and find its minimal polynomial

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A problem from Hungerford(galois theory)

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finite Galois extension

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Simple extension finder for $x^p-2$

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What's a minimal origami construction realizing a cube root?

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Find all roots of these two polynomials

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Check that the corresponding extensions are normal

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Is the extension $\mathbb{Q}(\alpha)/\mathbb{Q}$, where $\alpha = 2\pi i /3$, a splitting extension?

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List Question

Polynomial with Root $\pi+ei$

Irreducible Polynomial Field Extensions with Root $\cos \frac{2\pi}{7}$

How to prove irreducibility of this polynomial?

Prove that $x^2 − 2$ is irreducible over $\mathbb Q (\sqrt 3)$

Inverse of $2 − 3i \text{ in } \Bbb Q(i).$

Inverse of $α∈Z_3(α)$ where $α^3+α^2+2=0$

A proof needed in minimal polynomial.

Prove that $F(x)/F(\frac{x^3}{x + 1})$ is simple algebraic extension and find its minimal polynomial

A problem from Hungerford(galois theory)

finite Galois extension

Simple extension finder for $x^p-2$

What's a minimal origami construction realizing a cube root?

Find all roots of these two polynomials

Check that the corresponding extensions are normal

Is the extension $\mathbb{Q}(\alpha)/\mathbb{Q}$, where $\alpha = 2\pi i /3$, a splitting extension?

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