2.1. Horner’s Method^51
- 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.
- 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. - 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.
- 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.
- 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.
- (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.