Exploring End Behavior and Multiplicity in Polynomials

The video tutorial covers the degree of polynomials, explaining how to determine the degree by identifying the highest exponent or summing exponents in factored form. It discusses end behavior, showing how to determine if a polynomial is odd or even and positive or negative, and how this affects the graph's end behavior. The concept of multiplicity is introduced, explaining how exponents affect the graph's interaction with the x-axis. The tutorial includes examples of sketching polynomial graphs, focusing on degree, end behavior, and multiplicity.

What is the degree of the polynomial 5x^5 + 2x^3 - 4x^2 + 9x - 5?

• 3

• 6

• 4

• 5

If a polynomial is factored as (x-1)(x+2)^2(x-3)^3, what is its degree?

• 5

• 6

• 3

• 7

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

• Starts up and ends down

• Starts down and ends up

• Starts down and ends down

• Starts up and ends up

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

• Starts down and ends up

• Starts up and ends up

• Starts down and ends down

• Starts up and ends down

For the polynomial f(x) = -2x^7 + 3x^5 - x + 4, what is the end behavior?

• Starts down and ends up

• Starts up and ends down

• Starts down and ends down

• Starts up and ends up

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

• The graph makes a curvy turn at the zero

• The graph bounces off the zero

• The graph goes straight through the zero

• The graph has a vertical asymptote at the zero

If a zero has a multiplicity of 3, what does the graph do at that point?

• Goes straight through

• Bounces off

• Makes a curvy turn

• Has a vertical asymptote

Given the polynomial (x+1)(x-2)^2(x+3)^3, what is the end behavior?

• Starts up and ends down

• Starts down and ends up

• Starts down and ends down

• Starts up and ends up

For the polynomial (x-1)^2(x+2)(x-3)^3, what are the x-intercepts?

• -1, -2, 3

• -1, 2, -3

• 1, -2, 3

• 1, 2, -3

What is the degree of the polynomial (x-1)^2(x+2)(x-3)^3?

• 6

• 5

• 4

• 3