Let $\displaystyle \mathbb{C}[x]$ be the set of polynomials with complex coefficients. For every $\displaystyle p(x) \in \mathbb{C}[x]$ and $\displaystyle n \in \mathbb{N}$, there exist $\displaystyle q(x), r(x) \in \mathbb{C}[x]$ such that $\displaystyle p(x)q(x)=r(x^n).$ True or false?