Lots of good advice already, and we're all dealing with a lack of familiarity with your rifle, but here are some thoughts:
1. did you mount the scope yourself or was it professionally done? If yourself, re-check the torque on the screws. You should know what torque values the manufacturer of the base, the rings and the scope all call for, and make sure you've got that. Loose rings make it impossible to shoot consistent groups.
2. Check the torque on the action screws. Make sure you have them torqued to what is called out for the rifle/stock in question.
3. Check to see if your barrel is floating, or if it's touching your stock somewhere. Touching on one side could make it change point of impact as the barrel heats up.
4. Tell us a little about the ammo you're shooting -- have you had good results with it in other rifles, or is it a total unknown? If it's a total unknown, consider shooting some ammo that you know is capable of grouping.
5. If all this does nothing to get your rifle to group (and a new Rem 700 should shoot inside 2" at 100 yards with little tweaking), look into getting someone else to give it a few shots. Someone who you know shoots well, of course. As someone has already said, YOU are probably the biggest variable in your shooting and you might want to get a mentor or coach to advise you.
And by all means, keep us informed of what you learn and how it goes.