Worksheet: Rational Zeros Theorem

In this worksheet, we will practice using the rational zeros theorem to list all possible rational zeros in a given function.

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?

  • A 1 5 , 1 5
  • B 5 6 , 5 6
  • C 1 6 , 1 6
  • D−1, 1
  • E 6 5 , 6 5

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

  • A−2, 1 5 , 3
  • B2, 1 5 , −3
  • C−2, 3 5 , 1
  • D2, 3 5 , −1

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 ( 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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