How to find the zeros, intercepts, and multiplicity

The video tutorial covers polynomial analysis, focusing on finding zeros, understanding end behavior, and exploring multiplicity. It explains how to determine the end behavior of polynomials using the degree and leading coefficient, and demonstrates factorization techniques to simplify polynomial expressions. The tutorial also discusses the significance of multiplicity in graphing polynomials, helping students sketch graphs based on this information.

What does the end behavior of a polynomial with an odd degree and a positive leading coefficient look like?

• Rises left and falls right

• Falls left and rises right

• Falls left and falls right

• Rises left and rises right

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

• Find the derivative

• Calculate the integral

• Graph the polynomial

• Factor the polynomial

What common factor can be extracted from the polynomial T^3 - 4T^2 + 4T?

• 4

• T^2

• 4T

• T

What is the multiplicity of the zero at T = 2 for the polynomial T * (T - 2)^2?

• One

• Two

• Three

• Zero

How does a zero with a multiplicity of two affect the graph of a polynomial?

• The graph crosses the x-axis

• The graph remains above the x-axis

• The graph touches the x-axis and turns around

• The graph remains below the x-axis

Why is understanding the multiplicity of zeros important when sketching a graph?

• It determines the color of the graph

• It affects the slope of the graph

• It indicates where the graph crosses or touches the x-axis

• It changes the degree of the polynomial

What is the purpose of analyzing the end behavior and multiplicity when sketching a polynomial graph?

• To determine the polynomial's degree

• To find the polynomial's derivative

• To calculate the polynomial's integral

• To predict the graph's general shape and behavior