Expert: Paul Klarreich - 2/12/2011

Question
Can I factor x^3-7x-6? and if yes, how?

Answer
Questioner: Camila
Country: Canada
Category: Advanced Math
Private: No
Subject: Factoring
Question: Can I factor x^3-7x-6? and if yes, how?
........................................
I am not sure if you can.  I know I can, but I am much older than you and people who are very old know lots of stuff.

Such as:

1. The rational root theorem, which tells me to try plus-or-minus 1,2,3,6 because those are the divisors of 6.

2. Synthetic division, which gives me this result when I try x = -1:


1    0    -7     -6     (-1)
   -1     1     +6
-----------------------
1   -1    -6      0   << = P(-1)

3. The factor theorem, which tells me that  x+1 is a factor.

The rest you can work out.