Build any polynomial by placing zeros on the x-axis and setting how many times each zero repeats (multiplicity). Drag the rings. Watch what even and odd multiplicities do at the ground.
Tip: click a ring on the axis and drag. Near-multiplicity 2 = it touches the axis and turns around (a bounce). Multiplicity 1 or 3 = it punches straight through (a cross — but a triple flattens like an S on its side).
Unit 2 drills — build these with the tool:
Check yourself before you look: for each drill, say out loud where it crosses, where it bounces, and what happens at both ends. Then build it and see if the line agrees with you. The line never lies; your sketch sometimes does.