Polynomial Graphs and Their Multiplicities

What are the x-intercepts and their multiplicities for the following polynomial? f\left(x\right)=\left(x+3\right)\left(x+1\right)^2\left(x-1\right)

Tags

CCSS.HSF-IF.C.7C

• x = 1
  

• x = 1, 2

• x = 1, 3

• x = 2, 3

• x = 2

Tags

CCSS.HSA.APR.B.3

How many zeros does the polynomial function
 P(x) = 3x⁴+4x-8 have?

• 1

• 2

• 3

• 4

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞

• +∞
  -∞

• -∞
  +∞

• +∞
  +∞

In the above graph, which root has a multiplicity of 2?

• -1

• -3

• -120

• 4

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

Tags

CCSS.HSA.APR.B.3

y =  ^_(x + 2)(x - 1)² y = -(x - 2)(x + 1)² y = (x - 2)(x + 1)² y = -x³

• y =  ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³

Tags

CCSS.HSA.APR.B.3

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)

Tags

CCSS.HSA.APR.B.3

Which function might have the given graph?

• f(x) = (x - 6)(x + 4)²

• f(x) = (x - 6)²(x + 4)

• f(x) = (x + 6)²(x - 4)

• f(x) = x(x - 6)(x + 4)

Tags

CCSS.HSA.APR.B.3

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞

• +∞
  -∞

• -∞
  +∞

• +∞
  +∞