Final answer:
Finite differences can be used to find polynomial functions using methods such as Newton's Method, Lagrange Interpolation, Gaussian Elimination, and Synthetic Division.
Step-by-step explanation:
Finite differences can be used to find polynomial functions using several different methods. Newton's Method is a technique that uses divided differences to construct a polynomial that approximates a set of data points. Lagrange Interpolation is another method that constructs a polynomial that passes through a set of data points. Gaussian Elimination is a technique used to solve systems of linear equations, but it can also be used to find a polynomial that interpolates a set of data points. Synthetic Division is a method used to divide a polynomial by a linear factor.