R. E. Moore (“Interval Analysis,” Prentice-Hall, Englewood Cliffs, N. J., 1966) introduced the centered form for approximating the range of a rational function f over X, where X is a real interval. H. Ratschek (SIAM J. Numer. Anal. 17(1980), 656–662), introduced centered forms of higher order. These are, in general, better approximations than the centered form. If f is a polynomial p, however, then the centered form and the centered form of higher order lead to the same approximation. This distinguished behavior of polynomials is investigated and it is shown that the centered form is the best possible approximation of , if the centered form is compared with all approximations of that include and depend on the same data of p as those needed in constructing the centered form.