Consider the quadratic polynomial q(x)=3x2+kx+4, where k is an integer.
(i) Show that, for q(x) to split into two linear factors with integer coefficients, the number k2−48 must be a perfect square.
(ii) Determine all integer values of k that satisfy the condition obtained in part (i).
(iii) For each value of k found, factorise q(x) completely.