looks pretty nasty.
you can use some polish, but what sort and how depends upon how deep the scratches are. ideally, i would 'machine polish' them (ie: with a rotary or random orbital buffer), using a polishing pad and polish with some mild 'cut'.
instead of paint polish, you can also buy/use specific plastic polishes.
if you are not familiar with the above, and don't have easy access to them, you could try polishing buy hand, but it will take a lot more elbow grease and may not provide an as-new finish. you could use the same polishes as above, but more specifically, you could try:
*Meguiar's ScratchX (for paint, but should be ok for plastic)
*Meguiar's PlastX (specific for plastics)
but given the photo, i think a machine polish is in order. so you may need to employ a professional detailer to buff them up.