Saying that a polynomial has graph tangent to the x-axis at x= 0 and x= 1 means it has x= 0 and x= 1 are multi-roots of the polynomial and so it is of the form where i and j are larger than 1. (That is why there is the condition that " ".) Since p(x) is a general polynomial, it can be written in the form where k= n- i- j.