RRT says: Rational solutions can only be factors of 18 divided by factors of the coefficient of x^4. Rational roots therefore have the form:\[\pm 18, \pm9, \pm6, \pm3, \pm2, \pm1\]If you try (begin with the simplest, of course, so 1 or -1), you get -1 as a root.
You can now write f(x) as (x+1)(x³ ..........).
To get the 3rd degree part, you can do a long division or a synthetic division.
As soon as you have found it, you can do this trick again: I think 2 is a root as well (just try it),
so you can factor out x-2 to get (x+1)(x-2)(x²........). Now you can esily check if there are more rational or even real roots.