Hi gardenkitten,
You have a young Philodendron bipinnatifidum - also known as - Philodendron selloum,
young enough that it is not yet exhibiting the deeply cut foliage typical of a mature specimen.
This photo shows a young
plant, much like yours.
They go by many common names, including "
tree Philodendron", "Cut-Leaf Philodendron" and "Saddle Leaf Philodendron".
This site
(Floridata) has lots of info, including pictures of mature
plants.
Enjoy your new
plant.
**edit to add:
I don't think you'll have any problem getting it to grow lots of new roots.