Polynomial Degree and End Behavior

The video tutorial explains how to determine the zeros, multiplicity, degree, and end behavior of a polynomial function given in factored form. It covers the process of identifying zeros by setting each factor to zero, calculating multiplicity based on factor exponents, and finding the polynomial's degree by analyzing the leading term. The tutorial also discusses the end behavior of polynomials, using graphs to illustrate how the function behaves as x approaches positive or negative infinity.

What is the first step in analyzing a polynomial function in factored form?

• Calculating the derivative

• Finding the degree of the polynomial

• Identifying the zeros of the polynomial

• Graphing the polynomial

If a factor of a polynomial is (x - 4)^2, what is the multiplicity of the zero?

• 4

• 3

• 1

• 2

What is the multiplicity of the zero for the factor (x + 3)?

• 4

• 1

• 3

• 2

How do you determine the degree of a polynomial?

• By finding the constant term

• By adding the coefficients

• By counting the number of terms

• By identifying the leading term

What is the degree of the polynomial if the leading term is -8x^6?

• 6

• 4

• 5

• 7

Which factor contributes a degree of 2 to the polynomial?

• (2x + 1)^2

• (x + 3)

• (x - 4)

• (x - 2)

What does the end behavior of a polynomial function depend on?

• The leading term

• The sum of coefficients

• The constant term

• The number of zeros

If a polynomial has a negative leading coefficient and an even degree, what is the end behavior?

• Rises to both the left and right

• Falls to both the left and right

• Falls to the left and rises to the right

• Rises to the left and falls to the right

What is the end behavior of the function g(x) = -8x^6 as x approaches negative infinity?

• Approaches negative infinity

• Approaches positive infinity

• Remains constant

• Approaches zero

Which of the following is true about the end behavior of a polynomial with an odd degree and positive leading coefficient?

• Falls to both the left and right

• Rises to the left and falls to the right

• Rises to both the left and right

• Falls to the left and rises to the right