Polynomial

algebra

Definition

Polynomial

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Degree

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the polynomial.

Irreducibility

Irreducibility of a Polynomial

A polynomial $P(x)$ is called irreducible over a ring/field $R$, if there does not exist a factorisation:

$$P(x)=f(x)g(x)$$

where $f(x),g(x)\in R[x]$ (polynomial ring) with $\mathrm{deg}(f),\mathrm{deg}(g)\ge 1$.