Understanding Polynomial Zeros

The video tutorial explains how to find the zeros of a degree three polynomial function. It begins by identifying possible rational zeros using the factors of the constant term and leading coefficient. The tutorial then demonstrates how to use a graph to find real zeros and employs synthetic division to confirm these zeros and find remaining polynomial factors. Finally, it solves for complex zeros using algebraic methods, resulting in one real zero and two imaginary zeros.

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

• Use the quadratic formula

• List the factors of the constant term

• Perform synthetic division

• Graph the function

What are the factors of the constant term -16?

• +/-2, +/-4, +/-6, +/-8

• +/-1, +/-3, +/-5, +/-15

• +/-1, +/-2, +/-3, +/-4

• +/-1, +/-2, +/-4, +/-8, +/-16

How can we determine the possible rational zeros of the polynomial?

• By graphing the polynomial

• By using the quadratic formula

• By listing the factors of the leading coefficient

• By forming ratios of the factors of the constant term to the factors of the leading coefficient

What does the graph of the polynomial function help us identify?

• The degree of the polynomial

• The constant term

• The real rational zeros

• The leading coefficient

What is the real rational zero identified from the graph?

• X = 0

• X = -4

• X = 8

• X = 4

What method is used to confirm that X = 4 is a zero of the polynomial?

• Graphing

• Quadratic formula

• Trial and error

• Synthetic division

What is the degree of the remaining factor after dividing the polynomial by X - 4?

• Degree four

• Degree three

• Degree two

• Degree one

What equation is set to zero to find the complex zeros?

• X^2 = 4

• X + 4 = 0

• X^2 - 4 = 0

• X^2 + 4 = 0

What are the complex zeros of the polynomial?

• X = +/- 4

• X = +/- 2i

• X = +/- 2

• X = +/- 4i

What are the zeros of the given degree three polynomial function?

• X = 4, X = 2i, X = -2i

• X = 0, X = 2i, X = -2i

• X = 4, X = 2, X = -2

• X = 4, X = 4i, X = -4i