Given: A fourth-degree polynomial in x such as contains all of the powers of x from the first through the fourth. However, any polynomial can be written without powers of x. Evaluating a polynomial without powers of x (Horner's method) is somewhat easier than evaluating a polynomial with powers. Formula used: Expansion of a polynomial, Suppose, an equation is given in the form can be expanded and written as, This is known as expansion of an equation. Calculation: The given equation can be expanded as follow,
Therefore, the equation isan identifity. (b) Given: A fourth-degree polynomial in x such as contains all of the powers of xfrom the first through the fourth. However, any polynomial can be written without powers of x. Evaluating a polynomial without powers of x (Horner's method) is somewhat easier than evaluating a polynomial with powers. Formula used: Grouping of similar terms in a polynomial, Suppose, an equation is given in the form can be grouped and written as, This is known as grouping of an equation. Calculation: The polynomial, is grouped by the similar terms and written as follow,
Furhter, Therefore, the polynomial without powers is