An approximate polynomial is simply a polynomial with inexactly-known coefficients. You may have data with measurement errors that provides, after some kind of fitting, a polynomial that describes your data. You may have a formula with parameters for each coefficient, but the values of the parameters may be known only through experimental measurements. Approximate polynomials arise in many applied problems, from direct mathematical models through normal forms and bifurcation theory to geometric problems described in floating-point arithmetic for Computer-Aided Design.