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Polynomial Graphs: Zeroes and Their Multiplicities

The multiplicity of each zero is the number of times that its corresponding factor appears. In other words, the multiplicities are the powers. (For the factor x − 5, the understood power is 1.)
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How to Find Zeros & Their Multiplicities Given a Polynomial

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

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Zeros and multiplicity

Identify the Zeros and Their Multiplicities. y = x2 − 3x − 4 y = x 2 - 3 x - 4. Set x2 −3x− 4 x 2 - 3 x - 4 equal to 0 0. x2 − 3x−4 = 0 x 2 - 3 x - 4 = 0. Solve for x x. Tap for more steps x = 4 x = 4

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Multiplicity of Zeros and Graphical Consequences

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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