How to Determine All of the Zeros of a Polynomial

The video tutorial covers methods to find zeros of polynomials, including factoring, the rational zero test, Descartes' Rule of Signs, and synthetic division. It also discusses finding complex zeros using the quadratic formula. The tutorial emphasizes understanding the process of identifying possible zeros and verifying them through division techniques.

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

• Applying synthetic division

• Using graphing technology

• Factoring the polynomial

• Using the quadratic formula

What does the rational zero test involve?

• Finding the derivative of the polynomial

• Using the coefficients to find possible zeros

• Testing all integers as potential zeros

• Graphing the polynomial

According to Descartes' Rule of Signs, what can be determined?

• The exact number of zeros

• The sum of the zeros

• The degree of the polynomial

• The number of positive and negative real zeros

What is the purpose of synthetic division in finding zeros?

• To graph the polynomial

• To confirm if a number is a zero

• To simplify the polynomial

• To find the derivative

Why is it beneficial to use synthetic division over other methods?

• It does not require any prior knowledge

• It can be used for any polynomial

• It provides exact solutions

• It is faster and requires less computation

What type of zeros are found using the quadratic formula in this context?

• Both real and complex zeros

• Only real zeros

• Only complex zeros

• No zeros

What should be done if graphing technology is unavailable?

• Rely on synthetic division

• Use a calculator

• Use the quadratic formula

• Guess the zeros