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(a)First determine the powers of x needed for evaluating the polynomial.
(x - 7)x = (1.37 - 7)(1.37)
=-7.7131 Chopping to 3 digit arithmetic yields,
First, we can calculate the true value of the polynomial
at point x=1.37
Using 3-digits with chopping we have to calculate separately
The relative percent error is equal to
b)
Polynomial p can be expressed in a different way:
Now we calculate
The relative percent error is equal to
Therefore, the second form of polynomial is better for evaluation.
Answer is given below (on video)