This note provides the complete factorization of the Misiurewicz-Thurston polynomial q_l,n over C, which plays a central role in the study of the Mandelbrot set and Multibrot sets. The roots can be classified into two categories. First, there are hyperbolic points Hyp(k) for any divisor k of n, which are parameters whose critical orbits are of exact period k. Those are roots of q_l,n with multiplicity (d-1)[(l-1)/k]+2. Next are the points Mis(j,k) for 2<=j<=l whose critical orbits are pre-periodic of exact period k with an exact pre-period j. Those are simple roots of q_l,n.

Research supported by ANR-25-CE40-4532 (Smash).