That's quite clear, and there's a little reminder and a reference to this section when introducing algebraic equations pg. 255.
What about the case of 'K' discussed before, when can we use it and when we can't we? There are a few others: T, I, J, L, and optionally A-D (those are obvious). On pg. 57 it is written that A-D, I, J, K may be employed as general-purpose registers, so I'm still confused as to why it didn't work.
PS: 'K' (entered with alpha) and K (entered directly) are the same, correct? For what it's worth, I think that's part of what confused me when I tried the polynomial program of another user above.