Zeros and Multiplicities of Factored Polynomials

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This Demonstration explores the zeros of polynomials and their multiplicities on a graph. The zeros of a function are those values of for which . On the graph, the zeros give the locations of the intercepts.


The factor theorem states that is a zero of a polynomial if and only if is a factor of that polynomial, i.e. if and only if for some other polynomial . With that in mind, the multiplicity of a zero denotes the number of times that appears as a factor. For example, has a zero at of multiplicity 6. On the graph, the multiplicity of a zero tells you whether the function crosses the axis (in the case that the multiplicity is odd) or simply touches the axis (in the case that the multiplicity is even).


Contributed by: Laura R. Lynch (June 2014)
Open content licensed under CC BY-NC-SA



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