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Math Help - Factoring

  1. #1
    Super Member sakonpure6's Avatar
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    Factoring

    I have this advanced grade 11 factoring question y^4+2y^2+9 and i know the answer is (y^2+3-2y)(y^2+3-2y) however I do not know how to get there because when i first factored it i got y^2(y+1)(y-1)+9 which is wrong. Any help or tricks are appreciated!

    Thanks in advance!
    Last edited by sakonpure6; September 22nd 2012 at 08:17 PM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Factoring

    y^2+2y^2+9=3y^2+9=3(y^2+3)
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  3. #3
    Super Member sakonpure6's Avatar
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    Re: Factoring

    sorry i wrote down the wrong question.
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  4. #4
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    Re: Factoring

    Hello, sakonpure6!

    The answer you gave is wrong . . .


    \text{Factor: }\:y^4+2y^2+9

    We have: . y^4 + 9 + 2y^2


    Add and subtract 6y^2:

    . . y^4 {\color{red}\:+\: 6y^2} + 9 + 2y^2 {\color{red}\:-\: 6y^2} \;=\;(y^4 + 6y^2 + 9) - 4y^2

    . . . . . =\;(y^2+ 3)^2 - (2y)^2 . . . a difference of squares!


    Factor: . \big[(y^2+3) - 2y\big]\,\big[(y^2+3) + 2y\big] \;=\;(y^2 - 2y + 3)(y^2 + 2y +3)
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  5. #5
    Super Member sakonpure6's Avatar
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    Re: Factoring

    why did you choose to add 6y^2? can it be something else as long as we get a perfect square trinomial or...?
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  6. #6
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    Re: Factoring

    it's a algebra solving trick, I learn it in my 12th grade, where I learnt more techniques and procedures of trigonometry and other problem solving phenomenon. Most of problem and Solving Linear Equations With Fractions are also solved by using adding and subtracting.
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  7. #7
    Super Member sakonpure6's Avatar
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    Re: Factoring

    thank you but i still do not understand how Soroban came up with 6y^2 to add and subtract
    Last edited by sakonpure6; September 24th 2012 at 03:27 PM.
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