Again, do not have any idea where to start with this:

'Show that the subset of R[x]n (n should be subscript here), (n≥4), of those polynomials whose graph touch the x-axis tangentially at x=0 and x=1 is a vector subspace and find its dimensions. Also, find a basis for this subspace (If you cannot do the case of general n, try n= 4,5 first.)

Thanks in advance.