"College" Algebra on the train

Saw a gentleman in 20s-30s working with algebra problems on the train with headphone on and gee those look DIFFICULT. Yes, even for me (without pencil and paper). This homework involves solving equations with some 4-degree polynomials. Something like 3x^4-2x^3+3x^2+17 or something. Not obvious how to factor it at all. Fortunately that homework was multiple choice, and some choices have complex numbers a+bi in it (and of course the conjugate a-bi). The gentleman was helplessly trying to do "long division" trying to factor that thing. If I was to do that homework I would not don't bother factor that polynomial, plug in the choices to see which one solves the equation! I wanted to discuss math with this gentleman but he got headphone on.

Now that's one homework problem I want to protest about: It says, "Solve: x^2+2x+1=0" Come on, this is worded wrong, just what are we solving? It should say "Solve for x"

Given this gentleman's age and the nature of these unpractical problems it is very likely he is taking a class known as "College Algebra" or "Pre-Calculus" so he can brag to his friends who didn't attend college he is taking some serious stuff. I want to tell that gentlemen his calculus probably won't involve any complex things.

So that homework involves complex numbers, but in real life problems you rarely ever need to factor ugly polynomials and look for complex solutions, especially when the degree of polynomial > 2. So this is sort of pointless drills.

If teaching that subject I guess the goal is to tell them the beauty of being able to factor a polynomial will yield solutions. Not trial-and-error factoring an ugly polynomial pulled from thin air. Have they seen the glorious beauty of deriving the Cubic and Quartic formulas? and that there are no general solution after that? THAT'S glorious and enjoyable mathematics, the endless drill is not.

Oh and there is nothing "college" about complex numbers. Come on, define i=sqrt(-1) and there you go. High school students can do this. Perhaps Even elementary students. Why not? I propose whack this class completely and jam a bit more information into that first class of Algebra.

Complex numbers open a new important chapter of mathematics... i allows solving problems not solvable before, and its humble beginning is in the quadratic formula.