Appears to be johnson grass. A.K.A. crabb grass. Roundup works wonders. Just try not to get it on the good grass. Once it is dead you can fill in the dead spot with a piece of sod. A pre-emergent herbicide will prevent it from coming back from the seeds thrown off by the existing plants.
Dig it up fill in with play sand and cover with a nice piece of trimmed sod to fit the hole water well for week and it will look like nothing happened.
That's exactly what I had to do. Tried all sorts of weed-b-gone etc. It would just stun it for a while and come back. Make sure you get a little of the surrounding area as well. I think that stuff comes back even if a tiny bit of root is left.