\input zb-basic \input zb-matheduc \iteman{ZMATH 2015d.00810} \itemau{Kehle, Paul} \itemti{Colorful polynomial explorations.} \itemso{Consortium 106, 30-37 (2014).} \itemab From the text: Since the work of {\it K. Appel} and {\it W. Haken} [Bull. Am. Math. Soc. 82, 711--712 (1976; Zbl 0331.05106)], we have known that no map will require more than four colors if countries that share a border must receive different colors. Their proof finally resolved a conjecture first made in 1852. The history of the four-color theorem is fascinating and very accessible in {\it R. Wilson}'s [Four colors suffice. How the map problem was solved. Princeton, NJ: Princeton University Press (2002; Zbl 1030.05041)]. To work on a map-coloring problem we use a graph in which vertices represent the countries, and we join two vertices by an edge if the two countries share a border. The resulting graph will be a planar graph, meaning that it can be drawn so that no edges cross one another. A solution to a map-coloring problem is a proper vertex coloring of a graph: vertices joined by an edge are assigned different colors. \itemrv{~} \itemcc{K30} \itemut{graph theory; planar graphs; map-colouring problems; chromatic theory; vertex colourings of a graph; cycle graphs; chromatic polynomials; roots; edge-addition contraction principle; edge-deletion contraction principle; exploratory learning; student activities; chromatic uniqueness} \itemli{} \end