Deflating (factoring) a 6th degree polynomial

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What is the procedure to factor a 6th degree polynomial of a complex variable?

$$P(z)=1+x^2+x^3+x^4+x^5+x^6$$

I do have the correct answer but no idea how to get to it. The answer is:

$$P(z)=(z-w_7)(z-w_7^2)(z-w_7^3)(z-w_7^4)(z-w_7^5)(z-w_7^6)$$ where $$w_7=e^{i(2\pi/7)}$$

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Hint: $$(x^n-1)/(x-1)=1+x+\ldots+x^{n-1}$$