  Let Y_n(t) denote the set of all polynomials over the ring Z which are
reducible over the field Q and of degree n>1 and of height not greater than t.
We show that the true order of magnitude of |Y_n(t)| equals t^2 log t in the
special case n=2 and it equals t^n for each n>2. We also determine the true
order of magnitude of the size of certain interesting subsets of Y_n(t).
