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**Polynomial_Multiplicity.gsp**

This sketch is perhaps a handy tool for presenting the idea of multiplicity of polynomial zeros. The sketch shows a sixth degree polynomial defined by its roots, which are independent points on the x-axis. The dynamic environment allows us to see a continuum of functions as two roots are dragged closer to one another. In this way, one can develop an understanding of what a polynomial does near roots according to the multiplicity of that root. A root of multiplicity three, for example, can be recognized as the convergence of three roots. One can witness multiplicity as a special case in a coherent continuum.

The zeros on the sketch can be dragged with the arrow tool or directed to predetermined locations using buttons.

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