There do exist efficient root-finding algorithms for higher order polynomials.

The second order polynomial is calculated by the following double summation.

To handle irreducible 2nd order polynomials, can, in many cases, be approximated as .

Runge's phenomenon: high order polynomials can be highly oscillatory.

This method required the solution of a ninth order polynomial.

Within a given platform, the σ 2plots have similar general shapes that can be fitted well by low order polynomials.

Higher order polynomials yield better R 2values, but are probably not justified due to the noise in the data.

The purple line is a sixth order polynomial that best fits the blue boxes.

The first of these equations can be used to find the minimum (or maximum) of P. See second order polynomial.

Basis functions are linear or higher order polynomials.