We all know how important and ubiquitous polynomials are in mathematics. However, when faced with a (not so much in love with the subject) 14-year-old asking us why they should care about these things, answering that studying polynomials opens the door to more mathematics is probably not the best strategy. Of course, textbooks include some simple geometric and “real life” problems that can be tackled using polynomials, but they are far from exciting to solve.
How do/would you personally motivate your high-school students to study polynomials? More precisely, can you suggest
fun problems (not necessarily from everyday life) that can be solved using polynomials
interesting applications of polynomials (inside or outside of mathematics)
that might convince them that studying these sums of products of numbers and letters is actually worth it?