Weed ID

I've got this nasty weed in my back yard, and it's got these thick horizontal roots that are almost an inch in diameter at certain points.
So, 2 things

1) Can anyone ID it?
2) What's the best way of killing it?

I've been uprooting it as much as I can, but I'm starting to think that just cutting off the plant from the root might do.

Thanks everyone! Below are the links for the images!

http://cl.ly/3n3c1L320W2k3O3d1x0b
http://cl.ly/3j3H2i3A092e2x1K3M1D

 

It will probably be coming from a tree or shrub nearby, to which it is attached.

 

There's only one tree it could be attached to. Would it be easier to try to find the root leading directly to the tree instead of snapping off the further away weeds?

 

http://www.finegardening.com/how-to/qa/poplar-suckers-cause-chaos.aspx
http://www.esc.nsw.gov.au/weeds/Sheets/trees/T Poplar.htm
Populus nigra 'Italica' I believe.

 

If the sprouts are coming from the neighbor's tree, will this chemical kill the mother tree, too?

 

Seems unlikely, but it won't be good for the tree either.
I killed all the Oak suckers under my Live Oak for many
years and it never seemed to harm the tree.