How to use the rational zero test to determine all possible rational zeros

The video tutorial explains how to find all possible rational zeros of a polynomial by listing the factors of the constant term (P) and the leading coefficient (Q). It demonstrates forming combinations of these factors as P/Q, reducing fractions, and eliminating duplicates to finalize the list of possible rational zeros. The process involves understanding the rational zero theorem and practicing the method to ensure all potential zeros are considered.

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

• List all the factors of the leading coefficient.

• List all the factors of the polynomial's degree.

• List all the factors of the constant term.

• List all the factors of both the constant term and the leading coefficient.

Which of the following is a factor of Q in the given example?

• ± 6

• ± 24

• ± 9

• ± 12

How do you form the fractions to find possible rational zeros?

• By adding each factor of P to each factor of Q.

• By multiplying each factor of P by each factor of Q.

• By dividing each factor of P by each factor of Q.

• By dividing each factor of Q by each factor of P.

What should you do if you encounter duplicate fractions while listing possible rational zeros?

• Ignore duplicates and continue listing.

• Convert duplicates to decimals.

• Eliminate duplicates to simplify the list.

• Keep all duplicates to ensure accuracy.

Which fraction is reduced to 2/3 in the example?

• 4/9

• 12/9

• 8/9

• 6/9

Why is it important to write down all factors when finding rational zeros?

• To ensure no possible zero is missed.

• To practice multiplication skills.

• To make the process faster.

• To avoid using a calculator.

What is the final step after listing and simplifying all possible rational zeros?

• Graph the polynomial.

• Verify each zero by substitution.

• Check for any missing factors.

• Solve the polynomial equation.