8 ? 10x + 7x 2 ? 2x 3 + 3x 4 + 12x 5 , <?xml:namespace prefix = o ns = \"urn:sch

Question

8 ? 10x + 7x2 ? 2x3 + 3x4 + 12x5, <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /?>

when x is replaced by an arbitrary (but fixed) real number r.

For this particular instance, n = 5 and a0 = 8, a1 = ?10, a2 = 7, a3 = ?2, a4 = 3, and a5 = 12.

procedure PolynomialEvaluation1

(n: nonnegative integer;

r,a0,a1,a2,. . .,an: real)

begin

product := 1.0

value := a0

for i := 1 to n do

begin

product := product * r

value := value + ai * product

end

end

a) How many additions take place in the evaluation of the given polynomial? (Do not include the n ? 1 additions needed to increment the loop variable i.) How many multiplications?

b) Answer the questions in part (a) for the general polynomial a0 + a1x + a2x2 + a3x3 +

Explanation / Answer

question not clear

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