Consider the polynomial, p(x) = a0 + a1x + a2x2 + a3x3 where ai ≠ 0, ∀i . The…
2009
Consider the polynomial, p(x) = a0 + a1x + a2x2 + a3x3 where ai ≠ 0, ∀i . The minimum number of multiplications needed to
evaluate p on an input x is:
- A.
3
- B.
4
- C.
6
- D.
9
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Correct answer: A
Horner's method evaluates the polynomial p(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 as ((a_3 x + a_2)x + a_1)x + a_0. This structure requires exactly 3 multiplications, which is the minimum for this degree.