Polynomial Factor

A Factor of a Polynomial $P(x)$ of degree $n$ is a Polynomial $Q(x)$ of degree less than $n$ which can be multiplied by another Polynomial $R(x)$ of degree less than $n$ to yield $P(x)$, i.e., a Polynomial $Q(x)$ such that

$$P(x)=Q(x)R(x).$$

For example, since

$$x^2-1=(x+1)(x-1),$$

both $x-1$ and $x+1$ are Factors of $x^2-1$. The Coefficients of factor Polynomials are often required to be Real Numbers or Integers but could, in general, be Complex Numbers.

See also Factor, Factorization, Prime Factorization