I have posted this question earlier and had the answer given to me this way. But my teacher needs to know what type of factorization I used and I have tried to figure it out but have NO clue!!

Question

This is the question.
Solve the following inequality. write your answer in interval notation.
x^3+9x^2-108 less than or equal to o

My anser:
(x+6)(x+6)(x-3)
we have double zeros at x= -6
graph comes from way low and bounces back down off the x-axis at x= -6

Answer 1

Here is the rest of the answer:
then dropping down negative again

then it comes back up again and goes positive and crosses the x-axis at x=3
and from then on is positive

x=3
(-00,3)u(0,6)
**Now she says note that the last term does not contain an x. What type of method did I use in this posting. Explain this method. Can someone help me please

Answer 2

Not sure what you're going on about.
What do you mean "type of factorization"?
I used synthetic division to come up with the roots. If you have no clue, then you need to review finding roots of a function.

The roots are where the graph touches or crosses the x-axis.

The question is:

solve f(x) <= 0

The answer is:

f(x) <= 0 when x <= 3.
In interval notation, x is in (-oo,3]