VMO 2000 Problem 4

Given an angle α such that 0 < α < π, show that there is a unique real monic quadratic $x^2$ + ax + b which is a factor of $p_n$(x) = sin α $x^n$ - sin(nα) x + sin(nα-α) for all n > 2. Show that there is no linear polynomial x + c which divides $p_n$(x) for all n > 2.