I need help solving polynomial equations!

[SuperstarBarbie]

I have been surfing the internet all morning, and I abosolutely cannot! find anyone to help me solve this problem. It is x^3-5x^2+3x+9=0. I have not been able to pass this step. I have been staring at this equation for an hour, and I still can't figure it out. All I know is that it is not factorable, and you obviously cannot use the quadratic equation on this one. If you can help, it will be greatly appreciated. Thanks!
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Superstar Barbie!

 

[Loren]

You might try dividing the given cubic by a binomial. You know that for it to divide exactly, the constant term of the binomial will have to divide exactly into +9. That leaves you with the following as candidates.
x+1
x-1
x+3
x-3
x+9
x-9
You might try dividing your cubic by each of these to see if one of them can be a factor. If so, you might end up with a second degree trinomial that can be factored further. I happen to disagree with your statement that it can't be factored. I got it to factor into the product of three binomials.

 

[Denis]

To save you some time: (x^2 - 2x - 3) is result of division by (x - 3); OK?