Best ways in solving cubic equations without information on roots

[cheahchungyin]

Homework Statement

Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming

Homework Equations

The equation and attempt is shown in the image below, tell me if its unclear :shy:

The Attempt at a Solution

http://sphotos-a.ak.fbcdn.net/hphotos-ak-prn1/c67.0.403.403/p403x403/60637_450846098287003_1194154338_n.jpg

eventually found out x=7. Then by reducing the equation into a quadratic, I can find the other roots

So are there better ways in solving cubic? maybe some hacking fast ones? :D Appreciate the help!

 

[Dick]

You should try to find a rational root first using the Rational Root theorem. If you can find one, then you are practically done. Only if there aren't any would I resort to your technique.

 

[HallsofIvy]

In fact, doing that, it is easy to find three small integer roots.