To learn about the techniques for solving polynomials, including how to use the Rational Roots Test, try following the link provided in an earlier reply.
The lesson at that link will also demonstrate how much easier it is to divide out known factors, rather than guessing factors from the picture and then attempting to reconstruct the original factorization.
For instance, you'll learn how to divide out the x - 1, thus proving, when the remainder is zero, that x - 1 is actually a factor. Then, working from the now-simpler and lower-degree quotient, divide out the next factor. And so forth. Once you get down to a quadratic, you apply the Quadratic Formula.
Study the various examples in the lesson. They make the process fairly straightforward.