Multiplicity and Possible Real Roots of Polynomials

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 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)

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 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

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

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 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}