It's been a long time since I've worked on an explorer. So I don't remember if they are just black plastic or painted.
If they are plastic, then you would need to get some kind of conditioner and try that. If they are too far gone, then it's hopeless.
If they are painted, then treat them like you would your cars paint. You could give a good cleaner wax a try and see if that helps.
Hard to give advice without seeing the problem.