1. Literally, to smoothen or shine something through the use of forceful rubbing. In this usage, a noun or pronoun can be used between "polish" and "up." I'll need to polish up my shoes before John and Sarah's wedding tomorrow. Our rings are a bit tarnished—would you mind polishing them up for us?

2. To improve or refresh one's knowledge about or ability to do something. In this usage, a noun or pronoun can be used between "polish" and "up." I've been polishing my Japanese up before I go to Tokyo next month. I need to polish up on factorials before attempting to teach them on Monday.

3. To improve or refresh one's knowledge about or ability to do something. In this usage, a noun or pronoun can be used between "polish" and "up." I've been polishing my Japanese up before I go to Tokyo next month. I need to polish up on factorials before attempting to teach them on Monday.

4. To improve or refine the appearance something. I've been hearing rumors that there are going to be company-wide layoffs soon. Better start polishing up my résumé. We need to polish up this old house before any prospective buyers get here.