Polynomial Functions and Their Properties

The video tutorial explains how to find all zeros of a degree three polynomial function. It begins by listing possible rational zeros using the factors of the constant term and leading coefficient. The tutorial then demonstrates using a graph to identify real rational zeros and employs synthetic division to find polynomial factors. Finally, it uses the quadratic formula to determine complex zeros, emphasizing careful simplification.

What is the first step in finding the rational zeros of a polynomial function?

• Performing synthetic division

• Graphing the function

• Listing factors of the constant term and leading coefficient

• Using the quadratic formula

What are the factors of the constant term -78?

• +/-1, +/-2, +/-3, +/-6, +/-13, +/-26, +/-39, +/-78

• +/-1, +/-2, +/-3, +/-6, +/-12, +/-24, +/-36, +/-78

• +/-1, +/-2, +/-4, +/-8, +/-16, +/-32, +/-64, +/-78

• +/-1, +/-3, +/-9, +/-27, +/-81

Why is graphing used in finding real rational zeros?

• To calculate the derivative of the function

• To find the y-intercepts

• To determine the degree of the polynomial

• To identify the x-intercepts which are the real zeros

What does it mean if a polynomial has a degree of three?

• It has three variables

• It has three zeros, counting multiplicity

• It has three terms

• It has three coefficients

What is the purpose of synthetic division in this context?

• To simplify the polynomial

• To find the derivative of the polynomial

• To determine the degree of the polynomial

• To find another factor of the polynomial

What is the quadratic factor obtained after synthetic division?

• x^2 - 6x - 13

• x^2 + 6x + 13

• x^2 + 6x - 13

• x^2 - 6x + 13

Why is the quadratic formula used for the quadratic factor?

• To find the derivative

• To determine the degree

• Because it is not factorable

• Because it is factorable

What is the discriminant value in the quadratic formula for this problem?

• -16

• 16

• 0

• 36

What are the complex zeros of the polynomial?

• 4 +/- 6i

• 6 +/- 4i

• 3 +/- 2i

• 2 +/- 3i

What is the real rational zero of the polynomial?

• x = 3

• x = 6

• x = -6

• x = -3