Given polynomials: P(x) = 4x3 + 5x2 -2x + 3 Q(x) = 2x3 -3x2 + x + 1 Calculate the product PQ(x) in the following three ways.   Use standard algebraic polynomial multiplication (“big-FOIL” ) . Use Discrete Fourier Transform : Evaluate both P(x) and Q(x) at the eighth roots of unity. (check your notes if you don’t remember, but basically z = cos 45 + i sin 45, and all its “powers” in radical form!! Multiply the values for the above to generate 8 points, (z, PQ(z) ) for all powers of z.

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A: INTRODUCTION:

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A: In step 2, I have  provided  answer  with  brief  explanation-------------------

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