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Tenderloin-
Polystyrene should be fine to remove, assuming you've touched it and identified it as polystyrene. One of our bedrooms had them. Scrape off with a wallpaper scraper. If they didn't use too much adhesive then you should just be able to sand off the adhesive. However, often tiles are used to hide ceilings covered in cracks (as I discovered).
rodabod
Test for asbestos first. Search online and you'll find a link for a place that sends you a sampling kit with a mailer.