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Let p ( x ) be a polynomial of degree n , that is , p ( x ) = Pn i = 0 aixi.

Let p(x) be a polynomial of degree n, that is, p(x)= Pn
i=0 aixi.
(a) Provide the pseudocode for a simple O(n2) time method for computing p(x). Justify why your
pseudocode executes in O(n2).
(b) Now consider a rewriting of p(x) as
p(x)= a0+ x(a1+ x(a2+ x(a3+...+ x(an1+ xan)...)))
.
Provide the pseudocode for computing p(x) using the above formula. Provide the proof of cor-
rectness for your algorithm using loop-invariant method. State and justify the time complexity
of the algorithm.

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