MDF is available in 4’ X 8’ sheets. Compared to other types of material MDF is relatively inexpensive. It would best if you started with a full sheet so you would have no seem to worry with.
If you insist on using what you have, I recommend a wide backer-board of 6” or so. Other thin strips on each edge will keep the frame balanced against the wall.
If you insist on using what you have, I recommend a wide backer-board of 6” or so. Other thin strips on each edge will keep the frame balanced against the wall.