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Math Help - Inequality x^3-2x^2>4x-8

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    Inequality x^3-2x^2>4x-8

    2 questions.

    Explain how you could use a graph to solve inequality x^3-2x^2>4x-8.


    And

    What is the solution to x^3-2x^2>4x-8?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by booper563 View Post
    2 questions.

    Explain how you could use a graph to solve inequality x^3-2x^2>4x-8.
    graph f(x) = x^3 - 2x^2 and g(x) = 4x - 8. the interval(s) on which f(x) > g(x) is your solution.

    or, a harder way: graph f(x) = x^3 - 2x^2 - 4x + 8. the interval(s) on which f(x) > 0 is your solution.

    And

    What is the solution to x^3-2x^2>4x-8?
    without using graphs, note that the solution here is the same as the solution to

    x^3 - 2x^2 - 4x + 8 > 0

    note further that x^3 - 2x^2 - 4x + 8 = x^2(x - 2) - 4(x - 2) = (x - 2)(x^2 - 4) = (x + 2)(x - 2)^2

    can you finish?
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