Welcome to Android Central! Doing a factory reset would be a pretty drastic troubleshooting step to start off with. And if the battery itself is failing, it won't do anything.
Charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:
1. The main
Settings>Battery screen.
2. The fullscreen battery graph screen (which may show Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).
http://forums.androidcentral.com/gen...d-central.html You'll have to register first.
You might have to install a 3rd party battery monitor, like GSam Battery Monitor, to get the Cell Signal Strength graph.