Another way to evaluate a polynomial A(x) of degree-bound n at a given point x₀ is to divide A(x) by the polynomial (x − x₀), obtaining a quotient polynomial q(x) of degree-bound n − 1 and a remainder r, such that

A(x) = q(x)(x − x₀) + r.

Clearly, A(x₀) = r. Show how to compute the remainder r and the coefficients of q(x) in time Θ(n) from x₀ and the coefficients of A.