2. 30 points. Let A(x) = x² + 3x - 1 and B(x) = 2x-1. In this question, we will compute

the polynomial C(r) = A(r) B(r) by using the FFT algorithm.

(a) What is the minimum number of points we need to use? Explain.

(b) Evaluate A(z) at the complex 4th roots of unity. Show at least one level of recursion.

(c) Evaluate B(x) at the complex 4th roots of unity. Show at least one level of recursion.

(d) Compute C(r) at the complex 4th roots of unity.

(e) Find the coefficients of C(x).