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Tables

Finding Differences

There is a method that can be used to determine the degree of a polynomial just by using a data table. This method is called finite differences. To find the exact equation for the polynomial function, you need to find the coefficients by solving a system of equations or using some other method. This will be covered in later mathematics classes.

If you have a set of data with equally spaced x-values, you can find the lowest possible degree of a polynomial function that fits the data, if there is one, by analyzing the differences in the y-values. This technique, the finite differences method, determines only the degree of the polynomial. The steps are as follows:

Method of Finite Differences Algorithm

  1. List the terms as a sequence of numbers.
  2. Find the differences between successive terms until a constant is reached for every difference.
  3. Count the number of times it was necessary to subtract to get a common difference.
  4. The number of subtractions is the degree of the polynomial describing the sequence.