List questions from irreducible-polynomials

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A minimal polynomial problem that's bothering me

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Show that Matrix $M$ is diagonizable if the characteristic polynomial is irreducible

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Prove that if $x $ is transcendental over $F $ then $t^2-x \in F (x)[t] $ is irreducible

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Question about separable polynomial - proof verification

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Irreducibility of polynomial in $\Bbb F_p[x]$

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primitive polynomials of degree $d$ over $F_{3^3}$

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Evaluate an expression as an element of $F$

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A question about some polynomial

Published on 09 Apr 2026 - 15:53

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Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

Published on 11 May 2026 - 8:39

31

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A set of generators in disjoint cycle notation. Сompute the Galois group of an irreducible polynomial

Published on 15 Apr 2026 - 4:07

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Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

Published on 10 May 2026 - 15:10

470

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The Galois group of a specialized polynomial

Published on 21 Apr 2026 - 5:17

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Finding an irreducible polynomial of degree $n$ in $\mathbb Q[X]$ with real roots

Published on 10 May 2026 - 17:16

176

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$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

Published on 16 Apr 2026 - 19:44

List Question

Finding irreducible factors of $f=t^6-3$ for the fields $F = \mathbb{ Q, Z/5Z, Z/7Z}$

A minimal polynomial problem that's bothering me

Show that Matrix $M$ is diagonizable if the characteristic polynomial is irreducible

Prove that if $x $ is transcendental over $F $ then $t^2-x \in F (x)[t] $ is irreducible

Question about separable polynomial - proof verification

Irreducibility of polynomial in $\Bbb F_p[x]$

primitive polynomials of degree $d$ over $F_{3^3}$

Evaluate an expression as an element of $F$

A question about some polynomial

Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

A set of generators in disjoint cycle notation. Сompute the Galois group of an irreducible polynomial

Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

The Galois group of a specialized polynomial

Finding an irreducible polynomial of degree $n$ in $\mathbb Q[X]$ with real roots

$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

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