I have concluded after trying to make sense of how this topic is taught in Algebra classes, that it should be a separate subject like Trig or Geometry. Instead, I get the impression not only from W. Michael Kelley’s books, but from other sources online that many Algebra teachers are motormouthing their way through Polynomials. Maybe you might think I’m being unkind, if so, try wading through this stuff yourself. Remember that I read through the Chapters and did all the sample problems. I even substituted small numbers (2,3,4) for x,y,z in the equations. I came up with the answers but it barely made any sense.
I am not alone in this impression. I will quote the interactive mathematics website section on Polynomial Functions and Equations:
“…I propose we use Scientific Notebook (or some other Computer Algebra System) instead of the (quite useless) Factor and Remainder Theorems. (I have reluctantly included them in the next section…)”
“This is because the Factor and Remainder Theorems only work for ‘nice’ polynomials (that is, ones which have integer coefficients and so are easy to guess an initial root.)”
Right now, my plate is full and I’m making better progress in other areas, so I will come back to this at a later date.