Graph the polynomial given polynomial and using multiplicity and end behavior

The video tutorial covers solving polynomial equations by determining the degree, finding zeros, and understanding multiplicity. It explains how to calculate the degree by expanding terms and using the leading coefficient. The tutorial demonstrates finding zeros using the zero product property and discusses how multiplicity affects graph behavior, such as crossing or bouncing at intercepts. Finally, it guides on sketching the polynomial graph by hand, considering end behavior and x-intercepts.

What is the degree of the polynomial if the expanded form is X^3 * X^2 * -X?

• 5th power

• 7th power

• 6th power

• 8th power

How does the end behavior of a polynomial with a negative leading coefficient and even degree behave?

• Falls left, falls right

• Rises left, falls right

• Falls left, rises right

• Rises left, rises right

How do you find the zeros of a polynomial function?

• By setting the function equal to 1

• By multiplying all factors

• By dividing the function by its leading coefficient

• By setting the function equal to zero and solving each factor

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

• The graph has a vertical asymptote

• The graph crosses the x-axis

• The graph bounces off the x-axis

• The graph has a horizontal asymptote

What is the significance of a zero's multiplicity being odd?

• The graph has a hole at the zero

• The graph bounces at the zero

• The graph is undefined at the zero

• The graph crosses the x-axis at the zero

What is the first step in sketching the graph of a polynomial?

• Determine the end behavior

• Calculate the derivative

• Find the zeros and their multiplicities

• Identify the y-intercept

What is the relationship between zeros and x-intercepts in a polynomial graph?

• Zeros are different from x-intercepts

• Zeros are the same as x-intercepts

• Zeros are always positive

• Zeros are always negative