Multiplicity of a Polynomial

Which best describes the multiplicity of a root?

• It is the number of times the corresponding factor is repeated

• It is the highest degree of the polynomial

• It is the number of times x is multiplied by itself

• It is the number of x-intercepts on a graph

Find the correct statement about the zeros.

• −5 is a zero with multiplicity 1

• −5 is a zero with multiplicity 2

• −2 is a zero with multiplicity 1

• 2 is a zero with multiplicity 2

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

• -2, 7 multiplicity 3

• -2, 7, 3

• 2, -7 multiplicity 3

• 2, -7, 3

• 0, 2, -3

• 0, 2, -3 multiplicity 2

• 2, -3 mulitiplicity 2

• 0, -2, 3 multiplicity 2

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

• {0 mult. 3, 5, 2}

• {−2 mult. 3, 3, 1}

• {0 mult. 3, 3, 2}

• {2 mult. 3, 3, 3}

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

• {0 mult. 3}

• {0, 3, 1}

• {0, −2, −1}

• {−2, 3, 1}

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

Which of the following could be the equation of this graph in factored form? (Be careful and pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x+4)(x+1)(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

Which zero has an odd multiplicity?

• -4

• 4

• 2

• -2

How does a factor with multiplicity of 2 affect the graph of a polynomial function?

• Touch and bounce

• Straight Through

• "Snake" Through

• Touch, Flatten, and Turn