A polynomial of degree at most d is determined by its values at d+1 distinct rational points. If two such polynomials agree there, their difference has d+1 distinct roots. Each root a contributes a factor T-a; a nonzero polynomial of degree at most d cannot have that many factors. To recover coefficients c_0,...,c_d, write sum_k c_k*t_i^k=y_i for each known pair (t_i,y_i). These are linear equations in the unknown coefficients; exact rational elimination cancels one unknown at a time. Fewer values need not suffice: H(T)=2+3T+T^2 and H(T)+(T-1)(T-2) agree at 1 and 2 but give 2 and 4 at zero. In this exact interpolation task, data are not noisy regression observations.