For the following thinking question, please write a full solution including all work and explain your thinking process. Please note that a correct solution will not receive full marks, unless the solution is complete with all steps shown and explained. Determine the cubic function f(x) in factored form, with integral coefficients, such that it has the following properties:
a) the third differences are equal to 18
b( the remainder of f(x) divided by (x-2) is 27
c) x+1 is a factor
d) (1 ,6) is a point on f(x)