Polynomials are usually written as a sum of powers (or various products of generators) and Google gives me lots of results on how to get from that to the form that is a product of degree-$1$ polynomials (where you can see where the polynomial vanishes), e.g.,
$$ x^2 - 1 = (x + 1) (x - 1) $$
I am looking for the other direction though, which is much easier, but still computationally expensive if done naively.
I have an array of $n$ values that the polynomial vanishes on. Can I somehow get the coefficients in $n \log n$?
