calculus

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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!!

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

  • calculus -

    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

  • calculus -

    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]

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