Understanding Polynomial Zeros and Multiplicity

The video tutorial explains how to find zeros in polynomials, focusing on simplifying expressions and using the diamond method. It introduces the concept of multiplicity and how it affects graph interactions with the x-axis. The tutorial concludes by analyzing different graph scenarios to determine the correct answer.

What is the first step in simplifying the polynomial expression given in the video?

• Add a constant to the polynomial

• Factor out a common term

• Multiply the polynomial by a constant

• Divide the polynomial by a variable

Which method is used to factor the polynomial in the video?

• Diamond method

• Completing the square

• Synthetic division

• Quadratic formula

What does multiplicity indicate about a polynomial's graph?

• The y-intercept of the graph

• The number of x-intercepts

• How the graph interacts with the x-axis

• The degree of the polynomial

How does a graph behave at a zero with a multiplicity of 1?

• It bounces off the x-axis

• It crosses the x-axis like a straight line

• It forms a loop at the x-axis

• It does not touch the x-axis

What is the multiplicity of the zero at x = 2 in the video?

• 1

• 4

• 2

• 3

What is the zero of the polynomial with a multiplicity of 1?

• x = 1

• x = -1

• x = 0

• x = 2

How does the graph behave at a zero with a multiplicity of 2?

• It crosses the x-axis like a straight line

• It forms a loop at the x-axis

• It does not touch the x-axis

• It bounces off the x-axis like a parabola

What is the significance of the zero at x = 0 in the polynomial?

• It has a multiplicity of 2

• It has a multiplicity of 3

• It has a multiplicity of 1

• It is not a zero of the polynomial

Which graph correctly represents the polynomial's zeros and their multiplicities?

• Graph A

• Graph B

• Graph D

• Graph C

What is the final conclusion about the graph's behavior at the zeros?

• It crosses like a line at both zeros

• It bounces at both zeros

• It crosses like a line at x = 0 and bounces at x = 2

• It does not cross the x-axis