(a)To calculate: The value of P(2) without a calculator using both forms of the polynomial.
The value of P (2) is 236.
(b)The least amount of arithmetic operations was performed in (c) using
Horner's method.
FizeauV 2021-03-18Answered
(a)To calculate: The value of P(2) without a calculator using both forms of the polynomial.The value of P (2) is 236.(b)The least amount of arithmetic operations was performed in (c) usingHorner's method.
(a) 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 thanevaluating a polynomial with powers. Calculation: The polynomial, can be written as, without its power (Horner's method), and value of P(2) is given by, Further, Therefore, the value of P(2)is 236. (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. Calculation: Horner's method is the method of writing a polynomial without the powers of x and in its simplest form which makes the calculation much easier. therefore, the least amount of airhmetic operations was performed in (c) using Horner's method.