Once that is done, you'll be able to screencast your apps into videos in no time... Actually not. Even if the tablet is rooted, almost none of the screen recorder will work on the Asus Memo 10. That's a really sad situation and nothing will change as Asus is not providing any update for this device anymore.
There is one app that is working... SCR Pro! A while ago it was listed in the Google Play store but for some strange reasons, it was pull-out by Google. The author, iwobanas, created a thread to share his app for free on XDA (http://forum.xda-developers.com/showthread.php?t=2422061). I had already bought the app while it was listed on the Google Play store so I was happy to retrieve this amazing recorder when I had to reset my tablet.
The video quality is really good and you can even play some Minecraft while recording your screen. Optionally, your webcam can be display as an overlay. Internal sound does not seem to work but the microphone does.
Give it a try and if you like SCR Pro, please make a donation to the author.
You can download SCR Pro for free here: http://www.scr-screen-recorder.com/