Multiplicity of Polynomials

Which zero has an odd multiplicity?

• -4

• 4

• 2

• -2

Which root has even multiplicity?

• 1
• -4
• -1
• 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}

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

• (x + 5)³(x - 9)²(x + 2)(x - 4)

• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)(x - 4)

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}

State the zeros of the polynomial (include multiplicity):
f(x) = x⁴(x+3)²(x - 2)

•  0, 3, 2

•  0(multiplicity of 4), -3 (multiplicity of 2), 2

• -3 (multiplicity of 2), 2

• 0, 2 (multiplicity of 3)

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

• 2 (Mult of 3), 7 (mult 1)

• 0, 2, 7

• 2 (mult of 2), 7 (mult of 3)

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)

• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)(x - 4)

Even Multiplicities have which of the following effects on the x-axis?

• touches and bounces back

• wiggle

• crosses the x-axis

What is the equation in factored form of this graph?

• 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)