Polynomials

🌱

Definition

NumberTheory

Definition

Let $\mathbb{F}$ be a field and consider the ring $\mathbb{F}[x]$ of polynomials over $\mathbb{F}$ . Explicitly this is the set $\mathbb{F}[x]=\{ a_{0}+a_{1}x+\dots+a_{n}x^{n}:a_{i}\in\mathbb{F},n\ge0 \}$

Linked from

Associate

Irreducible (Polynomial)

Minimal Polynomial

Monic

Nonzero Constant Polynomials

Relatively Prime

Ring of Polynomials of Order p

Root

Degree is Closed under Addition

Division of Polynomials

Gauss's Formula

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

Irreducible Factorization

Lagrange Lemma

Unique Factorization Theorem for Polynomials