How to clean out old apps

[Planepics]

When I sync my iPad with iTunes on my Mac, when you click apps, it shows EVERYTHING i was crazy enough to once download. Can I get rid of the ones I don't want?? Many are long gone on the pad, and do show me the install button, but I want to get rid of them all together. What am I missing???
Also, When i have the app page up, it does NOT give me the option when I put my cursor over the app to hide it. It only gives me the option to download. And I tried moving the icon to the trash and that did not work either. (I AM talking about 3rd party apps).
Suggestions?????

 

[inkahauts]

I think if you hold down shift or something it'll let you hide it and you'd have to go in and I hide it on the account info pages so you'd really never see it again.