  In this note, we give a short, simple and almost completely self contained
proof of a classical result of Kaltofen [Kal86, Kal87, Kal89] which shows that
if an $n$ variate degree $d$ polynomial $f$ can be computed by an arithmetic
circuit of size $s$, then each of its factors can be computed by an arithmetic
circuit of size at most $\textsf{poly}\left(s, n, d\right)$.
  However, unlike Kaltofen's argument, our proof does not directly give an
efficient algorithm for computing the circuits for the factors of $f$.
