Polynomial Functions - Degree, Zeros and Multiplicities

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

• bounces off

• snake through

• straight through the x-axis

Tags

CCSS.HSA.APR.B.3

What is the multiplicity of an x-intercept (a.k.a. zero or root)?

• The highest exponent of a polynomial

• The number of different factors

• The exponent of the factor corresponding to that root

• The number in front of a polynomial

Tags

CCSS.HSF-IF.C.7C

Given
 $f\left(x\right)\ =\ 10x^2\left(2x-2\right)^3\left(x^2+3\right)$ ,
what is the multiplicity of  $x=0$  ?

• 10

• 3

• 2

• 0

Tags

CCSS.HSF-IF.C.7C

True or false: a root can have a multiplicity of  $0$ .

• True

• False

Tags

CCSS.HSF-IF.C.7C

Given  $f\left(x\right)\ =\ \left(2x\ +6\right)^7\left(x-3\right)^4$ ,
what is the multiplicity of the root  $x=-3$  ?

• 7

• 2

• 6

• 4

Tags

CCSS.HSF-IF.C.7C

Which root has even multiplicity? (Btw, this is the picture of one graph - you are just not shown the maximums and minimums.)

• 1

• -4

• -1

• 2

Tags

CCSS.HSA.APR.B.3

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

Tags

CCSS.HSF-IF.C.7C

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

Tags

CCSS.HSF-IF.C.7C

Select the 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)

Tags

CCSS.HSA.APR.B.3

Select the polynomial whose zeros and degree are given.

Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 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)

Tags

CCSS.HSA.APR.B.3