"Cultured marble" is actually polyester resin, which means that you can buff out light scratches using the same supplies and techniques a Corvette owner would use. At an auto parts dealer, buy a buffing pad that fits an electric drill, medium-cut rubbing compound, and paste wax made for fiberglass cars. Buff the surface with the compound and buffing pad, then rinse, apply the wax, and buff until shiny.

For severe scratches, look up "Bathtub and Sink Refinishing" in your telephone directory; these companies will sand the surface and recoat it with a special acrylic urethane.

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