Solving nonlinear inequalities?

Having trouble with a part of a math problem. It's been a couple of years since I've taken a math course and now I'm in a precal class that is conducted online so I just have a book to go from. Probably not the best choice on my part since math isn't a strong suit but I don't really have a choice. The problems are as follows:

(x-2)(x+4)(x-5)^2 is greater than or equal to zero

I know critical points at 2 and 4 but I'm not sure what to do about the (x-5)^2. Do I make it x^2+25 or does it just mean (x+5) and (x-5) are both critical points

Also the problem

x(x-2) / (x-4)(x+7) is less than or equal to zero

Again I know critical points are at 4 and -7 but I'm caught up on the x(x-2) do I make it x^2-2x.

Update:

Thanks but I'd really like to know how you came to get those answers. That would be more helpful.

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    -=-

    (-inf, -4], [2, inf)

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