Answer:
±{1, 2, 3, 6, 9, 18}
Step-by-step explanation:
You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.
Rational root theorem
The rational root theorem tells you the possible rational zeros are of the form ...
±{divisors of the constant term} / {divisors of the leading coefficient}
Here, the leading coefficient is 1, so its only divisor is 1.
The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.
The possible rational roots are ±{1, 2, 3, 6, 9, 18}.
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Additional comment
A graph shows the only real root is between 5 and 6, so none of the roots are rational.
