how to solve polynomial inequalities?

well i have this example

2x^3 - 15x < x^2

and i do know i have to get 0 on one side

2x^3 - 15x - x^2 <0

how do i factor it out? can i use the quadratic formula?

Update:

x(2x+5)(x-3)

that's exactly what i did , i wasn't sure if it was right though,

2 Answers

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  • 1 decade ago
    Favorite Answer

    One more step:

    Examine the curve: 2x^3 - 15x - x^2

    See ref: http://www.wolframalpha.com/input/?i=2x%5E3+-+15x+...

    And you'll see that the only time that the curve is negative is:

    x < - 5/2 ... and ... 0 < x < 3 ← your factors.

    So the final answer is: x < - 5/2 and 0 < x < 3

  • 1 decade ago

    ok that's a great start! so factor out an x:

    x (2x^2- x -15)

    This factors into: x (2x+5) (x-3)

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