Answer 8—A general N^th-order polynomial has the following form:  

This can be factored in the following way:
  

Specifically, a fourth-order polynomial would look like this:

Working outward from the innermost set of parentheses, each iteration consists of one multiplication by x and the addition of the next coefficient for a total of N multiplications and N additions. This is an especially efficient way to approximate arbitrary functions on DSP chips that have dedicated multiply-accumulate hardware.

Contributor: David Tweed