How can you clean and polish plastic automobile headlight lens.Toothpaste works,supposedly,any others is this?

My automobile has plastic headlight covers and over time they have become dull and not clear,due to road debris.I have been told that scouring them with toothpaste is one way to bring them back to transparency. Is there something else I can use to clean them.

If the discoloration is only on the outside, parts stores sell a cleaner with sponges and sandpaper that when the directions are correctly followed, works very well. They use an optical cleaner.

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