Degree and Multiplicity

The degree of a polynomial determines...

• the maximum number of x-intercepts

• if the end behavior is up or down

• the y-intercept

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

• touches and bounces back

• wiggle

• crosses the x-axis

Which root has even multiplicity?

• 1
• -4
• -1
• 2

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

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)

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

What is the multiplicity of the zero x=-5 for the function f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)?

• 1

• 2

• 3

• 4