USE FINITE DIFFERENCES TO DETERMINE THE DEGREE OF THE POLYNOMIAL

Finite difference :

The first-order differences of a polynomial function f(x) are found by subtracting function values for equally spaced x-values.

The second-order differences are found by subtracting consecutive first-order differences.

The third-order differences are found by subtracting consecutive second-order differences, and so on.

The following table gives values of several polynomial functions. Determine the degree of each polynomial.

Problem 1 :

Solution :

Since third difference are same, it is a third degree polynomial. The degree of the polynomial is 3.

Problem 2 :

Solution :

Since second difference are same, it is a quadratic polynomial. The degree of the polynomial is 2.

Problem 3 :

Solution :

Since third difference are same, it is cubic polynomial. The degree of the polynomial is 3.

Problem 4 :

Solution :

Since first difference are same, it is linear polynomial. The degree of the polynomial is 1.

Problem 5 :

Solution :

Since fourth difference are same, it is polynomial of degree 4.

Problem 6 :

Solution :

Since the second difference are same, it is a quadratic polynomial. The degree of the polynomial is 2.

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