mpc,
You may create a large dot pattern extending past the factor shape and expand it so you have individual dots, then simply delete the unwanted dots; you can do that in larger numbers, and decide whether each individual dot that is both inside and outside should extend past the factor shape or be deleted.
To create and expand the dot pattern, you may start with a single dot, then use Effect>Distort&Transform>Transform with a horizontal Move and many copies, then the same vertical move with many copies, then Object>Expand Appearance.