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Math Help - Polynomial inequality

  1. #1
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    Polynomial inequality

    Please check my answers.

    1. Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.

    (x - 3)(x + 2) > 0

    This is what I did:
    x-3=0 or x+2=0
    x=3 or x=-2

    The graph (-∞, -2) u (3, ∞)



    2. x^2-6x+5 > 0

    This is what I did:
    I factor it: x^2-1x-5x+5
    x(x-1) - 5(x-1)
    (x-1)(x-5)

    x=1 x=5

    The graph: (-∞, 1) u (5, ∞)



    3.x^2-3x-18<0
    This is what I did:
    I factor it: x^2+3x-6x-18
    x(x+3) -6(x+3)
    (x+3)(x-6)=0

    x=-3 or x=6

    The graph: (-∞, -3) u (6, ∞)


    4.x^2-3x-28 < or equal to 0
    This is what I did:
    I factor it: x^2+4x-7x-28
    x(x+4) -7(x+4)

    (x+4)(x-7)
    x=-4 x=7

    The graph (-∞, -4] u [7, ∞)


    5. x^2-4x < or equal to -3
    this is what I did:
    I added 3 to both sides, then got x^2-4x+3 < or equal to 0
    factor it: x^2-1x-3x+3
    x(x-1) -3(x-1)

    (x-1)(x-3)=0
    x=1 x=3

    this is the graph: (-∞, -3] u[-1, ∞)
    Last edited by soly_sol; October 28th 2007 at 08:19 PM. Reason: Left off graph
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  2. #2
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    Yeah it looks all right to me.
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  3. #3
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    Quote Originally Posted by soly_sol View Post
    ...
    5. x^2-4x < or equal to -3
    this is what I did:
    I added 3 to both sides, then got x^2-4x+3 < or equal to 0
    factor it: x^2-1x-3x+3
    x(x-1) -3(x-1)

    (x-1)(x-3)=0
    x=1 x=3

    this is the graph: (-∞, -3] u[-1, ∞)
    Hello,

    your calculations are OK but the graph is wrong: You added negative signs to your solutions
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