There is not a practical or effective way to fix or repair a deep scratch in this type of ceramic cook top. You can use the polish or creme that came with the cook top to clean the area, but that will not normally eliminate or mask a deep scratch. Using any type of sand paper or rubbing compound will not help either. Trying to repair the scratch with abrasives or epoxy can weaken the cook top and/or cause worse problems. Depending on the type and severity of the scratch, you may be able to use a mild kitchen polish such as Bar Keepers Friend to smooth out the scratch. Bar Keepers Friend is safe to use on ceramic cook tops and will not harm the surface. You can find this product at your local grocery store. Anything more abrasive than this is not recommended.