(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 2021-03-18 Answered
(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.
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hosentak
Answered 2021-03-19 Author has 100 answers

(a) Given: A fourth-degree polynomial in x such as 3x4+5x3+4x2+3x+1 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, P(x)=6x53x4+9x3+6x28x+12, can be written as, [((6x3)x+9)x+6]x8)x+12 without its power (Horner's method), and value of P(2) is given by,
P(2)=[((6.23)2+9)2+6]282+12
=[(18+9)2+6]282+12
=[54+6]282+12
=(1208)2+12 Further, P(2)=6(2)53(2)4+9(2)3+6(2)28(2)+12
=6.323.16+9.8+6.416+12
=19248+72+244
=236 Therefore, the value of P(2)is 236. (b) Given: A fourth-degree polynomial in x such as 3x4+5x3+4x2+3x+1 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.

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