Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0.

Rational root theorem:

Given a polynomial [tex]a_nx^n+a_{n-1}x^{n-1}+...+a_0[/tex], the rational roots are +-[tex] \frac{r_0}{r_n} [/tex] where [tex]r_0[/tex] = factor of the constant [tex]a_0[/tex] and [tex]r_n[/tex] = factors of the leading coefficient [tex]a_n[/tex].

So, to find the possible rational roots, we list all the factors of the constant and the leading coefficients and then set up the ratios.
In this case, the constant is [tex]a_0=–9[/tex] and the leading coefficient is [tex]a_n=1[/tex].
Factors of –9: +-1, +-3, +-9
Factors of 1: +-1

Thus, the possible rational roots are +-1/1, +-3/1, +-9/1
or +-1, +-3, +-9.

Answer: +-1, +-3, +-9