Lesson: Rational Zeros Theorem

In this lesson, we will learn how to use the rational zeros theorem to list all possible rational zeros in a given function.

Worksheet: 3 Questions

Q1:

Using the rational zeros theorem, you can list all the possible rational zeros of the function 𝑔 ( 𝑥 ) = 5 𝑥 − 6 𝑥 − 2 9 𝑥 + 6 3 2 .

What is the smallest possible rational zero?

What are the two possible rational zeros closest to zero?

What are the rational zeros, if any, of 𝑔 ( 𝑥 ) ?

Q2:

The rational zeros theorem can be used to generate a list of all possible rational zeros of a polynomial which we can then check one by one. How many possible rational zeros does the rational zeros theorem give us for the function ℎ ( 𝑥 ) = 9 𝑥 + 6 𝑥 − 2 𝑥 + 6 8 𝑥 − 2 7 𝑥 − 1 4 5 4 3 2 ?

Q3:

The rational zeros theorem can be used to generate a list of all possible rational zeros of a polynomial which we can then check one by one. How many possible rational zeros does the rational zeros theorem give us for the function 𝑘 ( 𝑥 ) = 9 𝑥 − 1 8 𝑥 + 3 5 𝑥 − 1 8 3 2 ?
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