Determine the Zeros of a Polynomial by Factoring

The video tutorial explains how to analyze polynomial functions by determining their end behavior, finding zeros, and understanding multiplicity. It covers the leading coefficient test, methods to find intercepts, and how multiplicity affects graph behavior. The tutorial provides a step-by-step approach to sketching polynomial graphs based on these concepts.

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

• Rises to the left and rises to the right

• Falls to the left and falls to the right

• Rises to the left and falls to the right

• Falls to the left and rises to the right

Which of the following is NOT a method to find the zeros of a polynomial function?

• Graphing

• Using the Pythagorean theorem

• Completing the square

• Using the quadratic formula

What is the first step in factoring a polynomial to find its zeros?

• Graph the polynomial

• Factor out the greatest common factor

• Use the quadratic formula

• Complete the square

What does the Zero Product Property state?

• If a product of factors equals zero, at least one of the factors must be zero

• If a product of factors equals zero, all factors must be zero

• If a product of factors equals zero, none of the factors can be zero

• If a product of factors equals zero, the product is undefined

How does a graph behave at a zero with an even multiplicity?

• The graph remains constant

• The graph touches the x-axis and turns around

• The graph crosses the x-axis

• The graph oscillates around the x-axis

What is the multiplicity of a zero if the factor is raised to the power of 2?

• 4

• 3

• 2

• 1

Why is understanding multiplicity important in graphing polynomial functions?

• It determines the color of the graph

• It affects the graph's behavior at the zeros

• It alters the leading coefficient

• It changes the degree of the polynomial