Will a factory reset remove spyware from my phone?

The answer to your question - Will a factory reset remove spyware is that the chances of malware surviving a factory reset are very, very small, but not zero.

If you have rooted your phone, there is a small chance that malware can copy itself to the system partition, so it would survive a factory reset. Some anti-theft software will do the same for legit reasons: if a thief steals a phone and performs a factory reset, the owner can still track the phone. If you are resetting the phone, you can do a firmware upgrade: download the latest firmware package from the phone manufacturer, and follow the instructions to upgrade the firmware. This will wipe out any trace of anything on the phone.