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50 2. Evaluation, Division, and Expansion

(b) A paper-and-pencil algorithm for making the evaluation in (a)

has the following table as its final result.

3 -4 7 2

9 15 66

3 5 22 68

Explain how the table is to be filled in and where the answer is

found.

(c) Show that the computation can be done on a pocket calculator

using one of the following two procedures, depending on the

calculator:

(9

Press buttons Result

3x3= 9

-4 = 5

x3 = 15

+7 = 22

x3 = 66

+2 = 68

(ii)

Press button Operator Result

3 Enter 3

3 Multiply 9

4 Subtract 5

3 Multiply 15

7 Add 22

3 Multiply^66

2 Add 68

This method of evaluating a polynomial is called Homer’s

Method.

2. Show that the Horner table for evaluating the polynomial 3t3 - 4t2 +
   7t + 2 at t = -2 is
   3 -4 7 2
   -6 20 -54

3 -10 27 -52

What is the required value? Check your answer independently.