Exploring Polynomial Zeros and Their Multiplicities

What color represents the graph of polynomial P1?

• Blue

• Green

• White

• Red

At which x-value does P1 first intersect the x-axis?

• x = 1

• x = 4

• x = 2

• x = 3

How many distinct zeros does P2 have?

• 4

• 3

• 2

• 1

What is the multiplicity of the zero at x = 3 for P2?

• 1

• 2

• 4

• 3

What happens to the graph of a polynomial at a zero with odd multiplicity?

• It touches the x-axis but does not cross.

• It crosses the x-axis.

• It bounces off the x-axis.

• It remains above the x-axis.

What happens to the graph of a polynomial at a zero with even multiplicity?

• It touches the x-axis but does not cross.

• It crosses the x-axis.

• It bounces off the x-axis.

• It remains above the x-axis.

What is the maximum number of zeros a third-degree polynomial can have?

• 4

• 3

• 2

• 5

What does the sign change around a zero indicate?

• No multiplicity

• Multiplicity of two

• Even multiplicity

• Odd multiplicity

How does the graph behave at a zero with multiplicity of two?

• None of the above

• Remains constant

• Touches and bounces off the x-axis

• Crosses the x-axis

What is true about the degree of a polynomial and its zeros?

• Degree is always less than the number of zeros

• Degree can be equal to or greater than the number of zeros

• None of the above

• Degree is always greater than the number of zeros