In some numerical computing applications, a desired computation is to find a polynomial that goes through a given set of points on a line, which, without loss of generality, we can assume is the x-axis. So suppose you are given a set of real numbers 

X = {x₀, x₁,...,x_n−1}. 

Note that, by the Interpolation Theorem for Polynomials, there is a unique degree- (n − 1) polynomial p(x), such that 

p(x_i)=0, for i = 0, 1,...,n − 1, 

and these are the only 0-values for the polynomial. Design a divide-and-conquer algorithm that can construct a coefficient-form representation of this polynomial, p(x), using O(n log₂ n) arithmetic operations.