factor X^3+X^2-6Xno

To factor
x^3+x^2-6x

Solution:

x^3+x^2-6x
= x*x^2+x*x-x*6

Each term is a factor of x. So we can
factor out x and rewite the given expression
as:

x(x^2+x-6)...............(1)

The
second factor x^2+x-6 in (1) by grouping the middle term   could be rewritten like: 
x^2+3x-2x-6=

=x(x+3)-2(x+3)

=(x+3)(x-2).
Substituting this for x^2+x-6 in (1), we get:

x(x+3)(x-2)
which is the factored form of  x^3+x^2-6