You'd probably start with x being the smallest integer:



I'd start with x being the middle one of the three: 



because it would be easy to multiply out (x-1)(x+1)

But heck! x is bound to be near the cube root of 26970,
So pick up a calculator that can take cube roots:



That's close to 30, so try 30 as the middle one

Try 29,30,31  

  <--That's it!

That's a quick way to get the answer, and since factoring 
and solving a cubic equation requires trial and error with 
synthetic division anyway, I'd say the above way is the 
best way to do it.  Other tutors might disagree.

Answer: 29,30,31

Edwin