If you didn't know that then perhaps it's be a good idea to first learn a little more about polynomials spaces:
Linear Algebra: More Vector Spaces; Isomorphism - CliffsNotes
Long story short, I proved = U+W.
U=(4s, 4t, -s, -t)
W=(i, j, 0, -j)
How do I find dimU and dimV? Or how do I find a basis for U and for W?
(and I'm pretty sure dimU=dimV=2 but I don't know how to prove it)
**I think I got it...
U=(4s,4t,-s,-t) = (4s, 0, -s, 0) + (0, 4t, 0, -t) dimU=2
W=(i, j, 0, -j) = (i, 0, 0, 0) + (0, j, 0, -j) dimW = 2
dimU + dimW = 4 = dim