Question 948077
Given: p(x) - q(x) = 0 has roots at x = 1, 2, 3


Therefore p(x) - q(x) = C(x-1)(x-2)(x-3) for constant C.


To simplify things, let C = 1. We can pick any cubic polynomials p, q with degree 3 that satisfy the constraint. A simple example is to let


p(x) = (x-1)(x-2)(x-3) + x^3
q(x) = x^3


Then p(i) = q(i) for i = 1,2,3, but p(4) = 70 and q(4) = 64.