The correct answer is $O(n * log₂ n)$.
The FFT is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse, in a much more efficient way than directly computing it by definition. When used for polynomial multiplication, the FFT can compute the product of two polynomials of degree-bound n in $O(n * log₂ n)$ time. This is significantly faster than the naive approach, which takes $O(n²)$ time.
The FFT-based method works by representing the polynomials in the point-value form, performing point-wise multiplication of the values, and then converting back to the coefficient form. This process is much faster than directly multiplying the coefficients of the polynomials.