(a) Differentiate \((x - 3)(x^{2} + 5)\) with respect to x.

(b) If \((x + 1)^{2}\) is a factor of \(f(x) = x^{3} + ax^{2} + bx + 3\), where a and b are constants, find the :

(i) values of a and b ; (ii) zeros of f(x).