To find a factor of f(x) we assume different values of x and substitute it in f(x)

First we consider the factors of the constant term −6 i.e., ±1,±2,±3,±6
Now we substitute the values of x in f(x)
If f(x)=0 for some value a
Then (x−a) is a factor of f(x)
[Note : This is a hit and trial method, So you have to iterate the process until you get the required x]

Substituting  x=−1 in f(x) , We get,
f(−1)=(−1)3+2(−1)2−5(−1)−6
=−1+2(1)+5−6
=−1+2+5−6
=−7+7
=0
∴ By factor theorem,
(x+1) is a factor of f(x)

Now dividing f(x) by (x+1), we get
x3+2x2−5x−6=(x+1)(x2+3x−2x−6)=(x+1){x(x+3)−2(x+3)}=(x+1)(x−2)(x+3)