Given that the polynomial x^2 - kx + 18 has only positive integer roots, find the average of all distinct possibilities for k.
+1223 18 = 1 * 18, 2 * 9, 3 * 6
(x - 1)(x - 18) = x^2 - 19x + 18
(x - 2)(x - 9) = x^2 - 11x + 18
(x - 3)(x - 6) = x^2 - 9x + 18
k = 19, 11, 9
average: 13
