## Definition ## In a [[commutative ring]] $A$, given a natural number $n:\mathbb{N}$ and a function $a:[0,n] \to A$ called the __coefficient__, a __degree $n$ polynomial__ is an endofunction $f:A \to A$ defined as $$f(x) \coloneqq \sum_{i:[0,n]} a(i) \cdot x^i$$ ## See also ## * [[power function]] * [[commutative ring]] * [[rational root theorem]] * [[function algebra]]