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Posted by on Saturday, January 1, 2011 at 5:18pm.

Please help me factor this.
x(-x^3-4x^2+3x+18) (using synthetic division please.) Thank You.

  • Math - , Saturday, January 1, 2011 at 5:31pm

    The possible rational factors are (+/-){factors of 18}/{factors of 1}: 18 is the coefficient of the x^0 term, and 1 is the coefficient of the greatest power of x - x^3 term.

    = (+/-){1, 2, 3, 6, 9, 18}/{1} = (+/-){1, 2, 3, 6, 9, 18}.

    Try factors using synthetic division until you find one that works. After, you will be left with a quadratic which is more easily factored.

  • Math - , Monday, January 3, 2011 at 4:51pm

    X(-X^3 - 4X^2 + 3X + 18).

    It was determined by trial and error
    that when X = 2, the quantity in paren-
    thesis = 0. Therefore,

    x = 2,
    x-2 = 0,

    Using synthetic division:
    (-X^3 - 4X^2 + 3X + 18) / (X - 2) =
    -X^2 - 6X - 9,
    Our Eq is now:
    X(X - 2)(-X^2 - 6X - 9),
    The trinomial = 0 when X = -3,
    X = -3,
    X + 3 = 0,

    Using synthetic division:
    (-X^2 - 6X - 9) / (X + 3) = -X - 3,

    Factored Eq: X(X - 2)(X + 3)(-X - 3).

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