A harder long division puzzle than the first; what should "Algebra I" solution look like?

Question

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine:

EDIT The problem is described below in the comments; additionally, NTRF is N times OGRE and ONOT is SLOG minus NTRF; the "A" is "brought down" per algorithm. Next two hunks explained similarly.