Question

Hello please solve this with steps

List the possible rational zeros of
f(x)= x^3-6x^2+6x-18 using the rational zero theorem

Answer 1

±{1, 2, 3, 6, 9, 18}

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.