Zoom while recording?

[Azure_Archer]

Hey all~

This is my first time looking for a camera for myself.. My family shares an ancient Kodak EasyShare C310, and I finally decided to upgrade 'a bit' for an upcoming convention I'm going to..

I'm looking for a something that can zoom while recording a video with audio. Preferably 4x or more optical zoom, at least 8mp, and somewhat compact. I'll be shooting landscapes and nature as well as indoors.. It'd also be a plus if it had night mode [though they all do, right?]

My budget's $250 and under if possible.

Please and thank you