Scratches can be buffed out of plastic. When baking soda and toothpaste fail, sandpaper usually does the trick as a plastic scratch remover. \
But when even sandpaper doesn't cut it to remove those scratches, a professional buffing machine will work. This machine works on a lot of different plastics. \
Of course, there are some types of damage that no tools can possibly fix. When your plastic is so deeply gouged that all the usual methods won't work, you might want to consider either replacing the item or finding a creative solution for covering up the damaged area. \
Maybe refinishing the chair entirely in something like washi tape can give the item brand-new life. Look for your own creative solution to scratches that won't buff out, and you may end up coming up with a super cool solution you never expected. \