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Worksheet: Finding Possible Rational Zeros of Polynomial Functions Using the Rational Zeros Theorem

Q1:

Using the rational zeros theorem, you can list all the possible rational zeros of the function 𝑔 ( π‘₯ ) = 5 π‘₯ βˆ’ 6 π‘₯ βˆ’ 2 9 π‘₯ + 6 3 2 .

What is the smallest possible rational zero?

What are the two possible rational zeros closest to zero?

  • A βˆ’ 1 5 , 1 5
  • B βˆ’ 5 6 , 5 6
  • C βˆ’ 1 6 , 1 6
  • Dβˆ’1, 1
  • E βˆ’ 6 5 , 6 5

What are the rational zeros, if any, of 𝑔 ( π‘₯ ) ?

  • Aβˆ’2, 1 5 , 3
  • B2, βˆ’ 1 5 , βˆ’3
  • Cβˆ’2, βˆ’ 3 5 , 1
  • D2, 3 5 , βˆ’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 β„Ž ( π‘₯ ) = 9 π‘₯ + 6 π‘₯ βˆ’ 2 π‘₯ + 6 8 π‘₯ βˆ’ 2 7 π‘₯ βˆ’ 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 π‘˜ ( π‘₯ ) = 9 π‘₯ βˆ’ 1 8 π‘₯ + 3 5 π‘₯ βˆ’ 1 8 3 2 ?