Unknown

2.1. Horner’s Method^51

3. In applying Horner’s Method, you should not fail to record zero coef-
   ficients. Check that the table for evaluating at t = 6 the polynomial

t5 - 4t3 + 2t2 - 7

is

1 0 -4 2 0 -7

6 36 192 1164 6984

1 6 32 194 1164 6977

and read off the required value of the polynomial. Check the value

independently.

4. Make up several polynomials of various degrees and evaluate them for
   a number of values of 1. Compare the number of operations required
   in Horner’s Method to the number that would be required for a term-
   by-term evaluation.


5. Programme a computer to carry out an efficient calculation of the
   value oft = 2.376 of the polynomial

4.82t5 f 87.2433t4 - 764.331t2 + 12.354t + 77.4412.

6. A student, evaluating a polynomial, presses the following buttons on
   his pocket calculator:

7x6~ x6=-2= x6=-3=x6=+1= x6=+2=

Find the polynomial being evaluated and the point of evaluation.

Determine the value of the polynomial.

7. Find the polynomial, the point of evaluation and the required value
   of the polynomial from the following table:

3 5 1 -2 6

6 22 46 88

3 11 23 44 94

Check your answer using a pocket calculator.

8. (a) Verify that

t4 + t2 - 3t + 7 = (t3 + 3t2 + lot + 27)(t - 3) + 88.

(b) Construct the Horner table for evaluating this polynomial at

t = 3. The last entry in the bottom row gives the value sought.

Interpret the remaining entries in the bottom row. Account for

your interpretation.