5.4 Multiplicity and Zeros

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

• touches and bounces back

• wiggle

• crosses the x-axis

Which zero has an odd multiplicity?

• -4
• 4
• 2
• -2

Which root has even multiplicity?

• 1
• -4
• -1
• 2

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

• 0, 6, -5
• 6, -5
• 0, -6, 5
• 1, -6, 5

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

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 2

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

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)

What are the roots of the polynomial function?
y = 9(x + 2)(x - 7)³

• -2, 7 multiplicity 3
• -2, 7, 0
• 9, 2, -7 multiplicity 3
• 2, -7, 3

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

• x = -4, x = 3, x = -2
• x = -4, x = 3, x = 2 
• x = -4, x = -3, x = 2
• x = 4, x = 3, x = 2