Master Determining all of the possible rational zeros of a polynomial, rational zero test

The video tutorial explains how to use the rational zero test to identify possible rational zeros of a polynomial. It begins with an introduction to the test and its usefulness in finding zeros when other methods are not applicable. The tutorial then defines rational zeros and distinguishes them from irrational and imaginary zeros. The main section covers the application of the rational zero test, detailing the process of identifying factors of the constant and leading coefficient, and calculating possible rational zeros. The video concludes with examples demonstrating the test and simplifying the results.

What is the primary purpose of the rational zero test?

• To determine the degree of a polynomial

• To simplify a polynomial

• To identify possible rational zeros of a polynomial

• To find all zeros of a polynomial

Which two components are crucial when defining rational zeros?

• The constant term and the leading coefficient

• The degree and the constant term

• The leading coefficient and the degree

• The constant term and the variable

What must be done to a polynomial before applying the rational zero test?

• Arrange it in ascending order

• Arrange it in descending order

• Factor it completely

• Convert it to a quadratic equation

How are the possible rational zeros determined using the rational zero test?

• By adding the factors of the constant and the leading coefficient

• By multiplying the factors of the constant and the leading coefficient

• By dividing the factors of the constant by the factors of the leading coefficient

• By subtracting the factors of the constant from the factors of the leading coefficient

What is the result of dividing the factors of the constant by the factors of the leading coefficient?

• The degree of the polynomial

• The possible rational zeros

• The irrational zeros

• The imaginary zeros

In more complex examples, what should be done with duplicate rational zeros?

• They should be multiplied

• They should be highlighted

• They should be removed

• They should be ignored

When the leading coefficient is larger than the constant, what is the approach to finding rational zeros?

• Only consider the constant's factors

• Ignore the leading coefficient

• List and simplify all possible combinations

• Use only the leading coefficient's factors