Let the polynomial $p$ be defined by $$p(x) = 2x^3-3x^2+4x-5$$ Suppose you evaluate the polynomial at $x=2$ using synthetic division (also called nested multiplication or Horner's scheme). You obtain an array that has three rows, with four entries in the first and third rows, and three in the second. The entries in the first row are (from left to right):
, , , and ,
The entries in the second row start in the second column, and are, from left to right:
, , and .
The entries in the third row are from left to right:
, , , and .