(d) Using a different algebraic method show that S(q) = 0. Hint: consider the equation x9 x = 0, and show that it factorizes into q linear factors over GF(q). Then calculate the coefficient of x9-1 in two ways. Note that q = 2 is a special case. [10] (d) Using a different algebraic method show that S(q) = 0. Hint: consider the equation x9 x = 0, and show that it factorizes into q linear factors over GF(q). Then calculate the coefficient of x9-1 in two ways. Note that q = 2 is a special case. [10]