(a) Factorize \(x^{2 n+1}-1\) as a product of real linear and quadratic polynomials.

(b) Write \(x^{2 n}+x^{2 n-1}+\cdots+x+1\) as a product of real quadratic polynomials.

(c) Let \(\omega=e^{2 \pi i / 2 n+1}\). Show that \(\sum \omega^{i+j}=0\), where the sum is over all \(i\) and \(j\) from 1 to \(2 n+1\) such that \(i