{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

I found that factoring [quadratic] trinomials, especially using the method of completing the square, was strangley inspirational for me.

I only wished you might become more comfortable compiling programs from the command line since I have a few programs that you could use in conjunction with paper and pencil to kind of check your work.  The completing the square program shows each step and can even handle irrational and complex roots.  I may have mentioned this already, but quite often, after I have gotten a program to produce correct results, I return to it and build into it "educational" components.  This often requires far more work than just producing sensible output.  In a real way, such effort is like a gift to my future self should I get a little rusty and need a crash course on these fundamental procedures.

Are you still using the Mac machine?   I'm certain that you could install the GNU g++ compilers since Mac uses the UNIX system.  I'm not pushing this on you, just leaving links for some rainy day, or a series of rainy days, if you ever catch the codemode bug.  Also see How to Install g++ on the Mac.

Of course, if this seems daunting and unnecessary, then I take no offense if you prefer not to bother with it.

Still, I am curious how you feel about factoring trinomials.   What methods do you use?  Trial and Error?   Grouping?  Completing the square?

For some reason, this was one of the fundamental procedures which I found very satisfying to go over thoroughly.

Take care.  You sound as though you have embraced the reality that this will be a very long process, and I am pleased to witness you keeping your feet on the ground and getting into whatever you study at the moment.  Years pass like months when it comes to studying math.   It's good that you are not racing, since we are always living only in the present moment.