ANSWER
The possible rational roots are [tex]\pm3[/tex] and [tex]\pm\frac{1}{3}[/tex]
EXPLANATION
According to the rational roots theorem, the possible rational roots of
[tex]9x^3+14x^2-x+18=0[/tex]
is given by all the possible factors of [tex]18[/tex] which are
[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]
expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is [tex]9[/tex] which are
[tex]\pm1,\pm3,\pm9[/tex]
in their simplest form.
One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.
This will give us
[tex]\frac{\pm9}{\pm3} =\pm3[/tex].
Another possible rational root is
[tex]\pm \frac{1}{3}[/tex].
Hence the correct options are
A and C.
Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.
