# How do you list all possible rational roots for each equation, use synthetic division to find the actual rational root, then find the remaining 2 roots for x^3-2x^2+9x-18=0?

The list of possible root are the divisors of 18 :
$\pm 1 | \pm 2 | \pm 3 | \pm 6 | \pm 9 | \pm 18$

Actually the polynomial given is factored quite easily

x^3-2x^2+9x-18=0=>x^2(x-2)+9(x-2)=0=> (x-2)*(x^2-9)=0=>(x-2)(x-3)(x+3)=0

Hence the roots are $2 , 3 , - 3$

Using synthetic division we have that

$$   1 -2 9 -18 | 2
1   -9  | 0


Hence $\left({x}^{3} - 2 {x}^{2} + 9 x - 18\right) = \left(x - 2\right) \cdot \left({x}^{2} - 9\right) + 0$