Learn How to Use the Rational Zero Test to Find the Zeros of a Polynomial

The video tutorial explains how to determine possible rational zeros of a polynomial using the rational zero test. It covers the process of listing potential zeros as P/Q, where P is the factors of the constant term and Q is the factors of the leading coefficient. The tutorial then discusses methods to verify which of these potential zeros are actual zeros, using graphing technology, synthetic division, and the remainder theorem. Finally, it demonstrates the verification process with an example, confirming the zeros and concluding the lesson.

What does the Rational Zero Test help determine?

• All possible rational zeros of a polynomial

• The exact zeros of a polynomial

• The degree of a polynomial

• The factors of a polynomial

In the Rational Zero Test, what does 'P' represent?

• Factors of the constant term

• The sum of the coefficients

• Factors of the leading coefficient

• The degree of the polynomial

What is the next step after listing all possible rational zeros?

• Graphing the polynomial

• Testing each possible zero using synthetic division or the remainder theorem

• Finding the derivative of the polynomial

• Solving the polynomial equation

Which method can be used to verify if a potential zero is an actual zero?

• Differentiation

• Integration

• Synthetic division

• Long division

According to the remainder theorem, if x = a is a zero, what is true about f(a)?

• f(a) = 1

• f(a) = 0

• f(a) = a

• f(a) = -1

What is the result of synthetic division if a number is a zero of the polynomial?

• A positive remainder

• A negative remainder

• A zero remainder

• A non-zero remainder

What are the actual zeros identified in the final section?

• 5, 4, and 3

• 1, 0, and -1

• 6, 3, and 2

• 3, 2, and 1