<s>[INST] Write in polynomial in factored form in complex number Write the following polynomial in factored form(in complex number):
$$1+z+z^2+z^3+z^4+z^5+z^6$$
Also, is there general solution of factoring for $1+z+z^2...z^n$ types of polynomial?
 [/INST] $$1+z+z^2+z^3+z^4+z^5+z^6=\frac{1-z^7}{1-z}$$
$$1+z+z^2+z^3+z^4+z^5+...+z^n=\frac{1-z^{n+1}}{1-z}$$
Denote $$1+z+z^2+...+z^n=S$$ then multiply by z we get
$$z+z^2+...+z^{n+1}=Sz$$ 
from firs equation subtract the second then solve by $S$
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