The rational root theorem states that if p/q is a zero of the function then p is a factor of the constant and q is a factor of the leading coefficient.

27 is the constant. Its factors are + or - 1, + or - 27, + or - 3 and + or -9.

1 is the leading coefficient. Its factors are + or -1.

You can make all the possible fractions p/q, then check each one to see if results in a 0 remainder when you divide the original function by it.

But you don't have to do that, because .

Take the cube root of both sides.

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