Actually screen recoding is done after root a device, but rooting your android have various process to do. You can record video without root the app called az screen recorder
Why az ,az screen recorder is best android application to Record videos with sound recoding ,you can speak record while screen recording .Thus app is working in android without any issues and problems
Also the app gives you strong video editor by which video can edited very well.
You can easily record videos of games ,tutorials etc with full HD quality
How to Record Android Screen
Download Az screen recorder from Google play store
After installing az recorder you need to also install az video editor plugins
Now you can start recoding screen on the go just with clicks
A bar appear in screen every time you open az recorder app
More about AZ
AZ Screen Recorder is the best app to record the screen of your Lollipop. It does NOT require root access, no time limit, no watermark, ad free and very easy to use with one action to start and stop recording.
This screen recording app will let you make beautiful screencast videos by providing every feature that you need in a simple and elegant user experience design.
★ Magic button : a button that controls your recording without showing anything on the screen. Thus, your video viewers will solely focus on the app, the game or whatever you want to screencast.
★ Overlay front camera : you can record your face and your emotions in a small overlay window, which can be dragged freely to any position on the screen and customized to any size and opacity.
★ Countdown timer : is there something you have to prepare before recording ? Don’t worry, the countdown timer will wait until you are ready to start and snap at the moment you want.
★ Draw on screen : this unique feature is huge when making a tutorial. You can emphasize, draw a symbol or mark something with any chosen colour directly on your screen.
★ Trim videos : the screencast can be long and contains unnecessary information, you can trim the parts you don’t want to make your videos even more impressive.
User also can edit videos like training videos , add music to videos , removing sounds , adding text in recorded video etc
Features are available in az video recorder app