Polynomials. Do we Really need to Teach/Learn them?

So why do we study polynomials? A Forbes author writes about how silly this is. https://www.forbes.com/sites/tomvanderark/2019/03/19/bad-bargain-why-we-still-ask-kids-to-factor-polynomials-and-how-we-fix-it/#7b98686063c1

The funny thing is, the study of (and more specifically, the factoring of) polynomials, including DesCartes Rule of Signs, finding upper and lower bounds of roots, determining end behavior, and the like used to fill up at least one-third of a standard Pre-Calculus class (not Algebra 2, btw, but Algebra 2 gets blamed for having this topic in its curriculum.)  But that was prior to about 1992. Currently I spend, maybe, a week at most in a PreCalculus class considering the behavior of polynomials so that students can progress to Calculus where they see applications of polynomials in economics (maximizing profit, minimizing loss) or physics (projectiles and quadratics, for example).  "Polynomials" has not really been a dominant topic since the advent of graphing calculators in the classroom -- about 1992.  Those of us over 40 remember factoring dominating the curriculum -- an accurate memory for that era-- but not accurate for what's currently taught.

In Algebra 1 (and some in Algebra 2), we teach factoring of quadratics, which are special polynomials. There's a bunch of reasons for teaching factoring of quadratics. 1. there's a good deal of number sense and problem-solving as well as organization of thinking that goes into this skill. (Number sense is important for things like understanding your bills, bank statements or making a budget.) 2. There's applications all over the place: projectiles, revenue maximization to name the most basic. 3. Students learn, at this level and in this place, how to symbolically represent expressions and equations in mathematics, a skill generalizable to science and even essay-writing.  4.  The graphs help all people understand how graphs work and what those graphs mean. It's hard to open a newspaper and NOT see a graph.  Many of those graphs actually show some level of embarrassing illiteracy regarding graphing, so these journalists could actually use a refresher course in Algebra 2 so they could represent that data well.  Each year when I see "factoring of quadratics" in the curriculum, I consider the fact that German high school students never learn factoring.  And they do fine.  So to be honest, I don't spend much time factoring quadratics.

Instead, "Dial Dallas," I say.  (Dallas is the home of the TI graphing and programmable calculator).  Students pull out their TI-84 and press Y=, 2nd Calc, and a few keystrokes later they have the roots.  Or the maximum value.  Or a specific value for a given independent value.  Anyone over 40 doesn't understand this process; those under 40 are all over it and can follow the routine in their sleep, answering complex questions that include interpolation and extrapolation.  One parent hired his son to do some analysis that I'd taught the son in class "for the office." The student returned to the classroom with a $300 check from his dad, letting me know his dad thought he'd gotten a good deal on information much more swiftly and less expensively than with a professional consultant.  "30 minutes," said the teen, "It took me 30 minutes."   I thought $600/hour was pretty good pay for a 16-year-old.

So what's my point?  People over 40 THINK they know what's in an Algebra 2 curriculum based on what they experienced over 20 years ago, but they don't.  How can they make good decisions when they simply do not have the necessary information?