I had a straggly little self-sown bit by the stream when I took on my plot. It developed into a great clump, and is now at the centre of a large area of black plastic. That should sort it!
Oh no it won't. I have been clearing an area that was covered in mypex membrane and the roots of all the invasive plants have grown and grown until they reach the edge. They are not lying under the membrane but in the soil itself. They are now a hard matting of roots that will not dig up without breaking and every small bit is a potential plant. The same thing will be happening under your plastic.
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