$$P(x) = (x-1)(x-\omega_{15})(x-\omega_{15}^2)...(x-\omega_{15}^{14})$$
Where $\omega$ is a root of unity of order 15 and $\omega_{15}= e^{2\pi i/15}$
I need to simplify this.
The solution is using fast fourier transform but I am not able to simplify it. The only lead I have is that 2 polynomials of same degree which have the same coefficient in front of the largest power and have same zeros are equal.
Any ideas on how to approach this problem?