Hello and welcome to Apple Support Communities, TonyMario.
It sounds like you're being prompted to enter the Apple ID of the previous owner of your iPad when using applications downloaded from the App Store. I know deleting and re-downloading apps so that you can use them properly is not an ideal situation. I can certainly understand why you would reach out for help with this.
If your iPad was set to factory settings and you installed all of the apps using your new Apple ID and not the previous owner's, it should not be asking you for the old Apple ID login. It's possible that after the iPad was reset, some apps were synced from iTunes on a computer to the iPad. If they were synced while signed into the previous owner's Apple ID, it would ask you for that Apple ID login when those apps needed to update. If this is the case, the only option is to delete the apps and re-download them using your own Apple ID information, like you have already been doing.
Another possible reason this may be happening is if your iPad has been restored from an iTunes or iCloud backup that was created with the iPad, or another iOS device, that was signed into the old Apple ID. If this is true with your iPad, erasing and re-installing the apps is the best solution as well.
I would recommend checking to make sure iTunes, App Store, and iCloud all show you signed in with the correct Apple ID, especially if your iPad was restored from a backup. To view which Apple ID is signed into iTunes and App Store, and to sign in/out of iTunes and App Store, follow the steps in this resource:
iPad User Manual: iTunes Store Settings
To view which Apple ID is signed into iCloud on your iPad, open up the Settings app and select "iCloud". If the old owner's Apple ID is listed there, follow the steps below to sign out. Keep in mind that some data on your iPad that was being synced with the previous owner's iCloud account may be removed from your iPad. If your iPad is in fact signed in with the previous owner's iCloud Apple ID and you are afraid of losing data, I would suggest creating an iTunes backup of your iPad and import your iPad photos to a computer using the steps found in these two articles:
How to back up your iPhone, iPad, and iPod touch
Import photos and videos from your iPhone, iPad, and iPod touch
- Scroll down and select "Sign Out", and then tap "Sign Out" again to confirm.
- Choose to keep or delete data when prompted.
Once you have signed out with the old owner's Apple ID, use that same screen to sign in with your new Apple ID.
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Have an awesome day!