Definition:Multiplicity (Polynomial)

Let $R$ be a ring.

Let $R \left[{X}\right]$ be the ring of polynomial forms over $R$.

Let $f\in R[X]$ be a nonzero polynomial.

An element $a\in R$ is said to be a root of multiplicity $n$ of $f$ if $(x-a)^n$ divides $f(x)$ in $R[x]$.

Catgeory:Polynomial Theory