Given two polynomials p(x) and q(x), the book's claim is that if p(x) = q(x)for allx, then the corresponding coefficients of p(x) and q(x) are the same. Of course, p(2) = q(2) is a weaker statement than p(x) = q(x) for all x (the latter implies the former but not the other way around), so it is not sufficient to guarantee that p(x) and q(x) have the same coefficients.