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Math Help - Another polynomial questions

  1. #1
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    Unhappy Another polynomial questions

    this is my problem:

    Show that the order you group terms when factoring a four-term polynomial does ot nake any difference. Give one example to illustrate this, showing the steps of both situations. I will be sooo glad when this class is over...I'm sooo completly lost! I truly appreciate all the help this site has provided me!
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  2. #2
    Senior Member topher0805's Avatar
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    Polynomial: x^3 + 2x^2 - 4x - 8

    Case 1: Group together the first two and the last two:

    (x^3 + 2x^2) - (4x + 8)

    Which gives us:

    x^2(x + 2) - 4(x+2)

    We then have:

    (x^2 - 4)(x + 2)

    And since (x^2 - 4) is a difference of squares we have:

    (x+2)(x-2)(x+2)

    Which equals:

    (x+2)^2(x-2)

    Case 2: Group the first with the third term and the second with the fourth:

    (x^3 - 4x) + (2x^2 - 8)

    Factor out common terms:

    <br />
x(x^2 - 4) + 2(x^2 - 4)

    Which gives us:

    (x + 2)(x^2 - 4)<br />

    Once again, a difference of squares:

    (x + 2)(x + 2)(x - 2)

    For a final answer of:

    (x + 2)^2(x - 2)<br />

    Both cases are equal.
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