Irreducible (Polynomial)

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Definition

NumberTheory

Definition

A polynomial $f\in\mathbb{F}[x]$ is said to be irreducible if $f$ is NOT divisible by any $g\in\mathbb{F}[x]$ where $1\le\deg g<\deg f$

Minimal Polynomial

Gauss's Formula

If an Irreducible Polynomial divides ab then it divides a or b

Irreducible Factorization

Unique Factorization Theorem for Polynomials