Polynomial Identities (Part 1)

Create a single coordinate-plane illustration that geometrically represents polynomial identities. Plot several polynomial function graphs and show, via parameter changes or an animation sequence, how polynomial multiplication and factoring lead to corresponding transformations in the curves. Add a polygonal shape or piecewise outlines in the plane, together with the important intersection relationships between the polygon and the graph(s), to highlight the symmetry properties that come from factoring. Construct by first setting up the coordinate system and the chosen polynomial functions, then drawing the polygon/key intersections to reflect the transformation links, and finally using slider-driven motion or a short animation to demonstrate the visual correspondence that supports the identity.