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.