Exploring Polynomials and Multiplicity

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

• Even

• Odd

• None

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3
• 3, -3, 4, 1
• 4, 1, -3
• 3, -4, -1, 3

Which root has even multiplicity?

• 1
• -4
• -1
• 2

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 with 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)

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

• x = 0, 3, 2
• x = 0, -3 (multiplicity of 2), 2
• -3, 2
• 0, 2 (multiplicity of 3)

• 2

• 1

• 4

• 3

• 1

• 2

• 3

• 4

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

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.