Exploring Zeros and End Behavior of Factored Polynomials

The video tutorial explains how to determine the zeros, multiplicities, degree, and end behavior of a polynomial function given in factored form. It covers identifying zeros by setting each factor to zero, calculating multiplicities based on exponents, finding the degree by analyzing the leading term, and understanding end behavior using the leading coefficient and degree. The tutorial also includes graphing techniques to visualize these concepts.

What are the zeros of a polynomial function?

• The points where the function has a minimum

• The points where the function has a maximum

• The x-values where the function value is zero

• The y-values where the function is undefined

If a factor of a polynomial is (x + 1)^4, what is the multiplicity of the zero at x = -1?

• 1

• 2

• 3

• 4

What is the zero of the polynomial function for the factor 5x + 1?

• -1/5

• 5

• -5

• 1/5

How do you determine the degree of a polynomial function?

• By finding the product of all exponents

• By counting the number of terms

• By identifying the term with the highest degree

• By finding the sum of all coefficients

What is the degree of the polynomial function if the leading term is 75x^11?

• 4

• 75

• 11

• 7

What determines the end behavior of a polynomial function?

• The multiplicity of the zeros

• The leading term

• The number of zeros

• The constant term

If the leading coefficient is positive and the degree is odd, what is the end behavior as x approaches positive infinity?

• The function values approach negative infinity

• The function values approach zero

• The function values approach positive infinity

• The function values remain constant

What is the end behavior of the polynomial function as x approaches negative infinity if the leading term is 75x^11?

• The function values remain constant

• The function values approach negative infinity

• The function values approach zero

• The function values approach positive infinity

How can you verify the end behavior of a polynomial function?

• By finding the sum of all coefficients

• By graphing the original function

• By counting the number of terms

• By finding the product of all exponents

What does the graph of the leading term 75x^11 indicate about the end behavior?

• As x approaches positive infinity, the function values decrease

• As x approaches negative infinity, the function values increase

• As x approaches positive infinity, the function values increase

• As x approaches negative infinity, the function values remain constant