Do I need to backup any user data before I perform a factory reset on a Chromebook?

In general, Chromebooks and their apps are designed so that no data is stored locally. All data should be stored either in Google Cloud or within the app. However, there is always the possibility that a user has stored some files locally and if that happens, the files will most likely be located in the My Files folder. You can view its contents by pressing the three keys simultaneously Shift+Alt+M. If you see any files in My Files, you can drag and drop them to Google Drive and they will be saved.