Practice with polynomial multiplication by FFT.
(a) Suppose that you want to multiply the two polynomials x + 1 and x2 + 1 using the FFT. Choose an appropriate power of two, find the FFT of the two sequences, multiply the results componentwise, and compute the inverse FFT to get the final result.
(b) Repeat for the pair of polynomials 1 + x + 2x2 and 2 + 3x.
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