Thanks! In case it helps: * Multiplying two polynomials as taught in school is in reality a convolution. * "performing the convolution of two signals in the time domain is equivalent to multiplying them in the frequency domain" * FFT allows us to convert from time domain to frequency domain * We use FFT to convert our polynomial to frequency domain. * If we are now in the frequency domain, we just need to multiply. Faster than a convolution.

Does it clarify the missing step? Happy to update the post with what's missing.