Polishes specifically made for plastics: Maguires, Novos, Turtle Wax, Polywatch, Mothers...
My personal recommendation is Abro Headlight Polish.
These will all remove fine scratches and ingrained dirt and discoloration.
The important thing to bear in mind is that Brasso, T-Cut, alcohols, or Acetone-based products are all way too harsh, and can totally ruin some plastics instantaneously!
Remember when LCD/LED TVs first hit the market? People used their bottle of Windex (Windowlene) and dissolved their screen on contact! Now they sell specific products for TVs.
Some so-called Polishes (Scratch Away) have built-in Rubbing Compounds and abrasive elements, these should be avoided too.
Don't be tempted to use whatever you have to hand at the back of the cupboard. It's worth taking the time, and paying the extra, to get the right product which will not harm plastics. Your car accessory store will stock a wide choice.
Finish with Carnuba Wax for a hard-shell, glossy shine that will protect and last.[this post was last edited: 12/9/2018-13:48]