Even multiplicity of a real root is indicated by the graph touching the x-axis. Uneven multiplicity is not easy to spot as the graph intersects with the x-axis This could indicate 1, 3 5 , etc. roots).

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The multiplicity of the roots of a polynomial f (x) can be determined in many ways. The basic method is to factorize the polynomial and count how many times each of the roots appears. It

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Polynomials have the property that if r is a zero of the polynomial p (x), then p (x) is divisible by x−r. The multiplicity of a zero is how many times you can divide out x−r from the

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In general, if a function has a zero of odd multiplicity, the graph of will cross the -axis at that value. If a function has a zero of even multiplicity, the graph of will touch the -axis at that point.

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How To: Given a graph of a polynomial function of degree n n, identify the zeros and their multiplicities. If the graph crosses the x -axis and appears almost linear at the intercept, it is a

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Find each zero by setting each factor equal to zero and solving the resulting equation.