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Problem 2. Use the FFT algorithm to evaluate f(x) = 8 − 4x + 2x 2...

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Advance Math

Problem 2. Use the FFT algorithm to evaluate f(x) = 8 − 4x + 2x2 + 3x 3 − 5x 4 − 4x 5 + 2x 6 + x 7 at the eight 8th roots of unitymod 17. You may stop using recursion when evaluating a linearfunction (a + bx), which is easier to do directly. The eight 8throots of unity mod 17 are 1, 2, 4, 8, 16, 15, 13, 9; it is easierto calculate with 1, 2, 4, 8, -1, -2, -4, -8. Do this by hand, andshow your work.

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