For the quadratic polynomial kx2+13x+k, k being a non-zero integer, answer the following.
(i) Show that, if the polynomial is factorable over the integers, then k must be a divisor of 13.
(ii) List all integer values of k that satisfy the condition found in part (i) and test each value to see whether the polynomial actually factorises over the integers.
(iii) State your final conclusion about the existence of non-zero integer values of k for which kx2+13x+k is factorable over the integers, giving reasons for your answer.