Question

x^4+x^3+x^2+x+1(x+1)

Answer 1

This quartic has four zeros, which are the non-Real Complex 5th roots of 1, as we can see from:

(x−1)(x4+x3+x2+x+1)=x5−1

So if we wanted to factor this polynomial as a product of linear factors with Complex coefficients then we could write:

x4+x3+x2+x+1

=(x−(cos(2π5)+isin(2π5)))⋅(x−(cos(4π5)+isin(4π5)))⋅(x−(cos(6π5)+isin(6π5)))⋅(x−(cos(8π5)+isin(8π5)))