Obtain the third degree of langranges interpolating polynomial method ?

To obtain the third degree of Lagrange's interpolating polynomial method, we need to have at least 4 data points. The third degree polynomial can be represented as:

P(x) = f(x0)*L0(x) + f(x1)*L1(x) + f(x2)*L2(x) + f(x3)*L3(x)

where L0(x), L1(x), L2(x), and L3(x) are the Lagrange basis polynomials of degree 3.

The Lagrange basis polynomials are given by:

L0(x) = (x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
L1(x) = (x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
L2(x) = (x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
L3(x) = (x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)

By substituting the given data points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)), and (x3, f(x3)) into the above equations, we can calculate the coefficients of the third degree Lagrange interpolating polynomial.