Roots, Factors, Multiplicities, and Graphs

Roots, Factors, Multiplicities and Graphs

How do I find the real roots and Their Multiplicities from a polynomial graph?

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How do I find the x-intercepts and Multiplicities of a factored polynomial?​

​Find all of the real roots (or solutions) of the polynomial from the graph.

​Find all of the real roots (or solutions) of the polynomial from the graph.

Multiple Choice

Find all of the real roots.

• 2, -6

• 6, -2

• -6, 6, 2

• -2, -6, 6

Multiple Choice

Which of the following is not a real solution to the graph shown?

• -5

• -2

• 0

• 1

​Multiplicity from a Graph: Cross, Bounce, and Wiggle

​Find the zeros and state their multiplicities.

​Find the zeros and state their multiplicities.

Multiple Choice

Find the zeros and state their multiplicities.

• -5, multiplicity: 2

  -1, multiplicity: 1

  0, multiplicity: 2

• -3.5, multiplicity: 2

  -1, multiplicity: 2

  1, multiplicity: 1

• -3, multiplicity: -2

  -1, multiplicity: -2

  1, multiplicity: 1

• -3.5, multiplicity: 2

  0, multiplicity: 2

  1, multiplicity: 1

Multiple Choice

Find the real zeros and state their multiplicities.

• -1.5, mult: 2

  0, mult: 1

  1, mult: 1

  4, mult: 1

• -1.5, mult: 2

  1, mult: 1

  4, mult: 1

• -0.5, mult: 2

  1, mult: 1

  4, mult: 3

• -2, mult: 2

  0, mult: 2

  1, mult: 1

  4, mult: 1

​Roots from Factors: Find the Roots from the Factors

​Roots from Factors: Find the Roots from the Factors

​Roots from Factors: Find the Roots from the Factors

Multiple Choice

Match the equation with the graph.

• $$\left(x+1\right)\left(x-7\right)^2$$  

• $$\left(x-1\right)\left(x+7\right)^2$$  

• $$\left(x+1\right)^2\left(x-7\right)$$  

• $$\left(x-1\right)^2\left(x+7\right)$$  

Multiple Choice

Match the equation with the graph.

• $$\left(x+2\right)^2\left(x-4\right)^2$$  

• $$\left(x+2\right)\left(x-4\right)$$  

• $$\left(x-1\right)^2$$  

• $$\left(x+2\right)\left(x-1\right)^2\left(x-4\right)$$  

Multiple Choice

Which equation represents the function?

• $$\left(x-6\right)^2\left(x+5\right)$$  

• $$\left(x+6\right)^2\left(x-5\right)$$  

• $$\left(x-6\right)^2\left(x+5\right)^2$$  

• $$\left(x+6\right)^2\left(x-5\right)^2$$