Finding Linear, Quadratic, and Cubic polynomials from Table
A polynomial in X is an algebraic expression of the form f(x) = a0 + a1x + a2x2 + a3 x3 +……….+ an xn, where a1, a2, a3….an are real numbers and all the indexes of ‘x’ are non-negative integers. Polynomial is derived from the words “poly” and “nomial,” which together mean “many terms.” Constants, variables, and exponents can all be found in a polynomial.
The highest degree of a polynomial’s exponent(variable) with a non-zero coefficient is its degree. The term “degree” means “power” in this context. Let’s look at different degrees of polynomials in this article.
The general linear, quadratic, and cubic functions are represented in the following three difference tables. These tables will be used to locate functions.
Using finite-difference tables, find the rule for each of the following sequences:
The function is a Linear of the form f(X) = ax + b. From the difference table for the quadratic
a = -1 and therefore a = -1 (using column 1st Diff 2)
Finally, a + b = 20 = -1 + b = 21 and therefore b = 21 (using column F(X))
∴ f (X) = -1X + 21