You'll need a proper glass polishing kit to shift scratches. The drill attachment and cutting paste kind of kit.
What I would say though, if a finger nail digs into a glass scratch, you will never polish it out. The best you can achieve is polishing out wiping arcs from gritty wiper blades but deep scratches, no chance!
Just throw a rock at it and get Autoglass round
They actually do a good job with the rain sensor, unlike a lot of other cheap glass outfits.