Garden Pests and Diseases: Please help with this beast!, 1 by Cheryl_IL

Cheryl_IL wrote:
I found a couple of these for the first time last summer. The smallest one that I dug up had a hooked root and I didn't get it all, but I haven't noticed that one come back. They're small now but got about 4' tall last year and grew very fast. They seem to be spreading by clump, and I probably had less than 10 of them in different parts of my yard. So far I've found only 3 this spring but it's still early.

Does anyone know what they are? Please tell me I can get rid of them, and how ?