Multiplicity and End Behavior of Polynomials

This is the correct end behavior model for the function
y = (x - 2)²(x² + 1)

• true

• false

These functions have the same end behavior model: y₁ = 3x⁵ + 2x³ + x - 1    and    y₂ = 3x²(2x³ + 4x + 2)

• true

• false

Which of these describes end behavior for the polynomial y = 3x⁵ + 2x³ - 7?

• a

• b

• c

• d

Find the zeros of this polynomial and describe their multiplicity.
f(x) = 3x⁴ - 12x²

• 0 multiplicity 3, -2 multiplicity 1, 2 multiplicity 1

•  -2 multiplicity 1, 2 multiplicity 1

• 0 multiplicity 2, -2 multiplicity 1, 2 multiplicity 1

• 3 multiplicity 4, -12 multiplicity 2

Which root has even multiplicity?

• 1
• -4
• -1
• 2

What could be the function for this graph in factored form?

• f(x) = (x-4)²(x+2)

• f(x) = (x+4)²(x-2)

• f(x) = (x-4)(x+2)²

• f(x) = (x+4)(x-2)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

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

• Even

• Odd

• None

If there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

• The function has an Even degree
• The function has a Negative coefficient
• The function has an Odd degree
• The function has 3 real zeros