Find the Zeros & Multiplicity of a Polynomial Function to Fifth Degree

The video tutorial explains how to find the zeros of a function and determine their multiplicity. It covers the process of factoring expressions, identifying perfect squares, and understanding the significance of multiplicity in zeros. The tutorial also demonstrates solving equations to find zeros and discusses how multiplicity affects the graph of a function.

What is the primary goal when finding the zeros of a function?

• To determine the maximum value of the function

• To find the input values that make the function output zero

• To calculate the derivative of the function

• To identify the asymptotes of the function

When you encounter a square number in a polynomial, what should you look for?

• A constant term

• A cubic term

• A perfect square or a difference of squares

• A linear factor

How does the multiplicity of a zero affect the graph of a function?

• It determines the slope of the tangent line at the zero

• It affects whether the graph touches or intersects the x-axis at the zero

• It changes the y-intercept of the graph

• It alters the domain of the function

What is the multiplicity of a zero if the factor is raised to an even power?

• Multiplicity of one

• Multiplicity of two

• Multiplicity of three

• Multiplicity of zero

What mistake do students often make regarding multiplicity and squared variables?

• Confusing multiplicity with the degree of the polynomial

• Believing multiplicity changes the domain

• Thinking multiplicity affects the y-intercept

• Assuming the variable's power determines multiplicity

What happens at a zero with a multiplicity of one on the graph?

• The graph touches the x-axis

• The graph has a horizontal asymptote

• The graph intersects the x-axis

• The graph has a vertical asymptote

If a factor is raised to the power of two, what is the multiplicity of the zero?

• One

• Zero

• Two

• Three