You can join broken plastic back together by using a soldering iron and then use a plastic spoon and melt the spoon so that you weld the broken plastic together.
Or you can also buy a plastic welding kit.
The plastic welding kit is basically a soldering iron with plastic welding rods that allow you to join most any types of broken plastic together.
J B weld is another option as J B weld when mixed right can joint plastic, metal and all sorts of materials and is some great stuff.
I've bought a plastic welding kit that came with the soldering iron as well as the plastic welding rods and it works great.
They are pretty cheap online such as through Amazon.