There is a patch of dirt on a hill covered with this plant (shown below). I'd like to pull them all out and make room for flowers and such. The second photo shows that the roots of this sucker go way down there. I'd like to pull them out completely rather than cutting, but on some of these I've yanked as hard as I can and they still won't budge. Any advice other than go to the gym?
From the shape of the leaves and the smooth, glossy texture of the leaves, I would say it's some kind of Holly.
Or it could be something like:
The secret of pulling any weed (plant) out of the ground (root and all) is to soak (via a garden hose) the ground really well beforehand, or go out there immediately after a really good down-pouring.
Then grab the weed (plant) firmly and as close to the soil line as possible, then pull slowly.
Once you've pulled a few inches of the weed (plant) out of the ground, move your hands back down the weed (plant), so you're once again grabbing it firmly and close to the soil line, then pull slowly. Repeat, repeat...
Pulling a plant with a very big tap root can be very difficult if not impossible. Water can help (I find it helps a lot with shallow weeds and grass), but you may well have to cut it.
Cutting the tap root as far down as possible with a sharp spade may be sufficient.
For good measure you could brush some "bush-b-gon" (woody plant) type weedkiller on the cut stem or root. This is usually sufficient to stop most things coming back and is extremely localized (ie. You won't kill anything else - unlike a spray).