What's a factor of x^3 - x - 6 =0

We will substitute with x=
2.

==> x^3 - x - 6 =
0

==> 8 - 2 -6 = 0

Then
x= 2 is a root for the equation.

==> (x-2) is a
factor.

Now we will divide by (x-2) to find other
factors.

==> (x^3 - x - 6) = (x-2) (x^2 + 2x+
3)

Now sine delta = (4-4*3) = 4-12 = -8 <
0

Then there are no Real roots foe the quadratic
equation.

Then the factors of the equation
are : (x-2) and (x^2 + 2x+3)