Eradicate Canadian Goldenrod (Solidago canadensis)?

My purple conflower erfly garden was invaded by Eradicate Canadian Goldenrod (Solidago canadensis). I spent this fall digging it up. Is this a rhizome plant ? How can I prevent its return? I am not certain if its pollen blew in wind dispersal or rabbits/critters brought it in. They are constantly in that garden. Help-advice?