Determine the multiplicity and zeros and graph of a polynomial

The video tutorial covers the process of sketching polynomial graphs, focusing on finding zeros and determining their multiplicity. It explains the use of the leading coefficient test to predict the end behavior of the graph. The tutorial emphasizes understanding the polynomial's degree and how it affects the graph's shape, including crossing and touching points. The instructor encourages using graphing technology but highlights the value of manual graph sketching for deeper comprehension.

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

• Perform long division

• Apply the quadratic formula

• Set the output equal to zero

• Use synthetic division

How do you determine the multiplicity of a zero?

• By the leading coefficient

• By the degree of the polynomial

• By the number of times the zero appears in the factorization

• By the constant term

What does the leading coefficient test help determine?

• The x-intercepts

• The end behavior of the graph

• The multiplicity of zeros

• The number of zeros

If a polynomial has a leading term of X^5, what can be inferred about its graph?

• It will have an odd degree behavior

• It will have an even degree behavior

• It will have a cubic shape

• It will have a parabolic shape

What is the significance of a zero with even multiplicity on a graph?

• The graph has a horizontal asymptote at this zero

• The graph crosses the x-axis at this zero

• The graph touches the x-axis at this zero

• The graph has a vertical asymptote at this zero

When sketching a polynomial graph, what is the importance of knowing the end behavior?

• To determine the y-intercept

• To understand how the graph behaves as x approaches infinity

• To find the exact coordinates of zeros

• To identify the turning points

Why might it be unnecessary to use graphing technology when sketching a polynomial graph?

• Because the graph is always a straight line

• Because the zeros and end behavior provide enough information

• Because the graph is always a circle

• Because the graph is always a parabola