Understanding Polynomial Graphs and Multiplicities

The video tutorial explains how to identify the roots or zeros of polynomials by examining their graphs. It covers the concept of multiplicity, distinguishing between odd and even multiplicities based on how the graph interacts with the horizontal axis. Two examples are provided: a degree five polynomial and a degree seven polynomial, illustrating how to determine the multiplicity of each root and ensuring the sum of multiplicities matches the polynomial's degree.

What is the y-value when x is -5 for the degree five polynomial?

• 0

• 10

• 5

• -5

How many roots does the degree five polynomial have?

• 5

• 2

• 3

• 4

What does it mean if a graph crosses the horizontal axis at a zero?

• The zero is undefined

• The zero has an odd multiplicity

• The zero has an even multiplicity

• The zero is not a root

If a graph appears almost linear at a zero, what is the multiplicity?

• Four

• Three

• Two

• One

What is the multiplicity of the zero at x = 0 for the degree five polynomial?

• Two

• One

• Three

• Four

What is the degree of the second polynomial discussed?

• Six

• Five

• Eight

• Seven

What is the multiplicity of the zero at x = -5 for the degree seven polynomial?

• Four

• Three

• Two

• One

How does the graph behave at x = 4 for the degree seven polynomial?

• Does not touch the axis

• Crosses the axis

• Remains above the axis

• Touches and bounces back

What is the sum of the multiplicities for the degree seven polynomial?

• Five

• Eight

• Seven

• Six

What is the multiplicity of the zero at x = 4 for the degree seven polynomial?

• One

• Two

• Four

• Three