Polynomial Functions and Their Properties

The video tutorial explains how to find the equation of a degree 4 polynomial function in factored form. It starts by identifying the rational roots from the graph's x-intercepts and then uses these roots to write the polynomial in factored form. The tutorial further explains how to determine the constant 'A' by using the y-intercept of the graph. Finally, it solves for 'A' and presents the complete polynomial function, discussing the expected behavior of the polynomial based on its degree and leading coefficient.

What is the maximum number of real rational zeros a degree 4 polynomial function can have?

• Two

• Three

• Four

• Five

Which of the following are the x-intercepts of the polynomial function discussed?

• (0, -3), (0, -1), (0, 2), (0, 5)

• (3, 1), (-2, -5)

• (-3, 0), (-1, 0), (2, 0), (5, 0)

• (-3, -1), (2, 5)

How do you determine the factors of a polynomial function from its zeros?

• By using the opposite sign of the zeros

• By subtracting the zeros

• By adding the zeros

• By multiplying the zeros

What is the y-intercept of the polynomial function used to find the constant 'A'?

• (-15, 0)

• (15, 0)

• (0, -15)

• (0, 15)

If one of the zeros is x = -3, what is the corresponding factor?

• x - 1

• x + 1

• x + 3

• x - 3

What is the value of 'A' after solving the equation using the point (0, -15)?

• -1/2

• 1/2

• -2

• 2

What is the complete factored form of the polynomial function?

• F(x) = -1/2(x - 3)(x - 1)(x + 2)(x + 5)

• F(x) = 1/2(x - 3)(x - 1)(x + 2)(x + 5)

• F(x) = -1/2(x + 3)(x + 1)(x - 2)(x - 5)

• F(x) = 1/2(x + 3)(x + 1)(x - 2)(x - 5)

What is the behavior of the polynomial function as it moves to the left and right?

• Approaches zero

• Approaches negative infinity

• Approaches positive infinity

• Remains constant

What is the degree of the polynomial function discussed?

• 2

• 3

• 5

• 4

What is the sign of the leading coefficient of the polynomial function?

• Positive

• Negative

• Zero

• Undefined