  A polynomial form is established for the off-shell CHY scattering equations
proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam
invariants provides a new expression for the polynomial scattering equations,
immediately valid off shell, which makes it evident that they yield the
off-shell amplitudes given by massless $\phi^3$ Feynman graphs. A CHY
expression for individual Feynman graphs, valid even off shell, is established
through a recurrence relation.
