Determine the Zeros of a Polynomial by Factoring

The video tutorial explains how to determine the end behavior of polynomial functions by identifying the degree and leading coefficient. It covers finding intercepts and zeros using various methods like factoring and the quadratic formula. The concept of multiplicity is introduced, explaining how it affects the graph's behavior at zeros. The tutorial provides a step-by-step approach to sketching the graph based on these properties.

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

• Rises to the left and falls to the right

• Falls to the left and rises to the right

• Falls to the left and falls to the right

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

• Factoring

• Completing the square

• Graphing

• Using the Pythagorean theorem

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

• Graph the polynomial

• Complete the square

• Use the quadratic formula

• Factor out the greatest common factor

If a factor of a polynomial is (x - 5), what is the corresponding zero?

• x = 5

• x = 0

• x = 10

• x = -5

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

• The graph crosses the x-axis

• The graph touches the x-axis and turns around

• The graph has a vertical asymptote

• The graph is undefined at that point

How does an odd multiplicity affect the graph at a zero?

• The graph crosses the x-axis

• The graph is undefined

• The graph has a hole

• The graph touches the x-axis and turns around

What is the multiplicity of a zero if the factor is (x - 0)^2?

• 1

• 2

• 3

• 4