Multiplicity of Polynomials

Find the correct statement about the zeros.

• -2 is a zero with a multiplicity 1

• 2 is a zero with a multiplicity 2

• -5 is a zero with a multiplicity 1

• -5 is a zero with a multiplicity 2

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

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Label the graph based on the multiplicity of the zero(s)

a

b

Multiplicity = 2

Multiplicity = 1

This point is not a zero.

Multiplicity = 0

What is/are the zero(s) and the multiplicity for this 3rd degree polynomial in the graph?

• x = 0, multiplicity 1

• x= -1, multiplicity 2

  x =1, multiplicity 1

• x = 0, multiplicity 3

• x = -1, multiplicity 2

  x = 0, multiplicity 1

How does a multiplicity of 1 affect the graph?

• Crosses with a bend

• bounces off

• cross straight through

Which root has even multiplicity?

• 1

• -1

• 2

• -4

If the graph of a function crosses the x-axis with a bend, what does that mean about the multiplicity of that zero?

• odd

• even

• none

If the graph touches the x-axis and then bounces back in the other direction, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

What could be the equation of the polynomial function shown in this graph? (write the equation in factored form first and then convert it to standard form)

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In the figure above a polynomial of a degree 6 is graphing. What are the zeros and their multiplicity?

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