Thank you for asking about poly-coated paper. Again whether an item is recyclable or not depends on where you live. Call your recycling service provider and/or city/county agency that contracts with the service provider and ask them about recycling guidelines for your area.
Poly-coated paper in simple terms is plastic coated paper (examples: paper plates/cups with a shiny finish, cardboard with a shiny coating/packaging). Since it is difficult for a recycling company to separate two recyclables from each other (in this case paper and plastic) it makes it very difficult to recycle most poly-coated paper. It often winds up gummy/gooey clump in the pulper at the paper recycling mill. The paper and cardboard are recyclable but the thin sheet of plastic is hard to recycle.
I hope this helps! Thank you for recycling!