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

Q1:

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 π ( π₯ ) = 9 π₯ β 1 8 π₯ + 3 5 π₯ β 1 8 3 2 ?

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 β ( π₯ ) = 9 π₯ + 6 π₯ β 2 π₯ + 6 8 π₯ β 2 7 π₯ β 1 4 5 4 3 2 ?

Q3:

Using the rational zeros theorem, you can list all the possible rational zeros of the function π ( π₯ ) = 5 π₯ β 6 π₯ β 2 9 π₯ + 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 π ( π₯ ) ?

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