I would think schools prefer one textbook. I would also prefer one textbook, if only because of the costs. One textbook would probably be cheaper that two textbooks, right? On the other hand, if you only need the second half of the book, because you already mastered the first half, two textnooks would be better, because then you could only buy the second one.

If the second book is much harder than the first, then spliting them would be a great idea. I wouldn't mind a 600 page book, I would prefer it. But since this is for younger people, then spliting is a good idea. It would be similar to vol.1 and vol.2. And it wouldn't be as intimidating, as you said.

As for schools, they might prefer one book and they might not. I'm sure you know, that every few years (sometimes 'every 10 yrs'), school boards have meetings to choose textbooks (and syllabus, etc) according to the statistics of the student population. In other words, how the student are doing in a subject, namely math. The Peel school board (the area where I live), has lowered the math standards due to low averages, and because students are having difficult with the topics.
So keeping this in mind, the reasons they would prefer one book is because it covers all important algebra topics, it has varying difficulty of questions, it gives good examples, it has lots of proofs, its well written, easy or a bit challenging, etc.
The reasons a school board might not pick a 600 page book over a 300 pg is, well its long, the teachers might not be able to get through the material in a term/ semester, students might get confused over some topics and slow down the whole sylabus, what topics to teach and what not to, etc.
If you plan 2 books, then as long as they are planned out with a simple layout, and the correct order of chapters (easiest to hardest, most useful to least at that stage of development, etc), then there is a very big chance they will get picked over other textbooks. There are obviously other things to consider too, like how many questions there are, detail, explanations, ease to understanding, etc.
I wish Peel board would consider AoPs books, the are more interesting than the monotone textbooks we study.

As for length of book, I think the Intro Algebra alone will be closer to 700 than 600. Another factor to consider is wieldiness. A 700-page 8.5" by 11" book (paperback, no less) will be very unwieldy. For example, most of the reference books I have for programming are this size or larger. They're fine for looking things up for a minute here or there, but to use on a continual basis (not to mention carry around), they'd be a nightmare.

I assume the Intro to Algebra is equivalent to Algebra 1 in a typical school curriculum? In which case 2 volumes might be a tough sell. I just checked the Algebra book both my kids used. It is an excellent text written by Harold Jacob, which is very popular in the homeschooling community. It is 860 pages, including selected answers. It is a hard covered book, and seems quite an acceptable size.

I agree it might be less desirable to have a book that large in softcover. Would be sturdy enough? It might make more sense to go hardcover instead of two volumes. OTOH, some school districts are starting to worry about the weight of books kids are forced to carry in their backpacks, so a two volume paperback might feed into that concern.

From Mr. Rusczyk's description of the topics I think it will definitely cover at least from the beginning of Algebra I through Algebra II.

Yep, actually it might even pass for pre calc as well (throw in limits, polar, parametric, vectors, and so forth...er, maybe pre calc is pushing it a little bit ).

Ordinarily you would have two large textbooks for Algebra I and Algebra II. However, there is usually a couple chapters devoted to review (i.e. both books will cover a lot of the same stuff). Additionally, they have an insane amount of mostly mundane practice problems. Does a book really need that many? Essentially what this does is force the teacher to pick and choose problems. Thus if there were some problems you think are important or interesting, they will get passed over by some teachers.

I'm not really sure which would be better. However, a 700 page book sounds incredibly daunting for a middle schooler if you ask me (even the advanced ones). The task of working through those 700 pages will be easier to digest if it's broken into two parts, in my opinion.

For subject coverage, the combined book would cover 90% or so of Algebra I and II, and all the algebraic portion of pre-algebra.

860 pages for an algebra I book sounds like a haul for the students - I'm guessing that book must have some material that's in our other books (and probably plenty of 'pre-algebra', whatever that is).

One reason standard textbooks are so long is that they have to cover standards for a zillion different districts, so they end up bloated with material that many students will never even look at. We try to avoid that and not have tons of repetition. As joml noted, a student going from algebra 1 to algebra 2 to pre-calculus will see 200 pages of algebra textbook repeated in the algebra 2 book, and 200 pages of algebra 2 repeated in pre-calculus (if not more). Again, part of this is because the major publishers have to create one-size-fits-all books. We're not doing that - we're trying to fit one particular size: good students who like math.

From lfm's comments, we'll have to make clear that the Volume 1 and Volume 2 mimics an algebra I - II series to a large extent. The Intermediate Algebra covers what little bit of Algebra 2 the Intro doesn't cover (matrices might be about it), then moves on to pre-calculus and beyond.