How to Determine the Multiplicity and Zeros of a Polynomial

The video tutorial explains how to find the zeros of a polynomial function and determine their multiplicity. It begins with setting the function to zero and finding the greatest common factor (GCF). The instructor then demonstrates factoring the expression using perfect square trinomials. The zeros are found using the zero product property, and their multiplicity is discussed. The tutorial concludes with an explanation of how the graph behaves at these zeros.

What is the first step in finding the zeros of a polynomial function?

• Determine the degree of the polynomial

• Set the function to zero

• Find the derivative

• Graph the function

What is the purpose of identifying the greatest common factor (GCF) in a polynomial?

• To graph the polynomial

• To determine the leading coefficient

• To simplify the polynomial

• To find the degree of the polynomial

Which of the following is a characteristic of a perfect square trinomial?

• It has three distinct terms

• It can be factored into a binomial squared

• It has a degree of three

• It is always positive

How do you solve for zeros using the zero product property?

• Set each factor equal to zero

• Take the derivative of the function

• Graph the function

• Multiply all factors together

What does a multiplicity of 2 indicate about the graph of a function at that zero?

• The graph touches the x-axis but does not cross

• The graph crosses the x-axis

• The graph is undefined at that point

• The graph has a vertical asymptote