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Thread: four term polynomial with gcf

  1. #1
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    four term polynomial with gcf

    Hi all;
    I need to factor 16x^3y^3 +16 - 8y^3 - 32x^3 which is a four term polynomial with a common factor of 8, giving 8(2x^3y^3 +2 -y^3 - 4x^3) rearranging the poly in the brackets so they can be grouped gives 2x^3y^3 - y^3 - 4x^3 +2.


    Which gives a factored version of (8y^3 - 16)(2x^3 - 1).

    But if I rearranged the polynomial differently 2x^3y^3 - y^3 + 2 - 4x^3

    I end up with 8y^3(2x^3 - 1) + 16(1 - 2x^3) the binomials are different why?

    Thanks.
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  2. #2
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    Quote Originally Posted by anthonye View Post
    Hi all;
    I need to factor 16x^3y^3 +16 - 8y^3 - 32x^3 which is a four term polynomial with a common factor of 8, giving 8(2x^3y^3 +2 -y^3 - 4x^3) rearranging the poly in the brackets so they can be grouped gives 2x^3y^3 - y^3 - 4x^3 +2.


    Which gives a factored version of (8y^3 - 16)(2x^3 - 1).

    But if I rearranged the polynomial differently 2x^3y^3 - y^3 + 2 - 4x^3

    I end up with 8y^3(2x^3 - 1) + 16(1 - 2x^3) the binomials are different why?

    Thanks.

    8y^3(2x^3 - 1) + 16(1 - 2x^3) = 8y^3(2x^3 - 1) - 16(2x^3 - 1) = (2x^3 - 1)(8y^3 - 16)
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  3. #3
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    Ok I see what you did but more explanation please.
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  4. #4
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    Quote Originally Posted by anthonye View Post
    Ok I see what you did but more explanation please.
    what's to explain? the two expressions that you said are "different" are the same.
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  5. #5
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    Yeah I see now, Also in a four term polynomial you dont have to take out the common factor before grouping do you and can the grouping method be applied to all even term polynomials.
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