find the factorization for a compex polynomial

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I have a question about finding the factorization for the complex polynomial: $P(z)=z^{10}-z^9+z-1$. It is easy if $z \in \mathbb{R}, P(z)=(z^9-1)(z+1)$. However, I am not sure if this is true for $z\in\mathbb{C}$. Thanks!