Long Division...3

Discussion in 'Algebra' started by nycmathguy, Jul 15, 2022.

  1. nycmathguy

    nycmathguy

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    College Algebra
    Chapter 1/Section 4

    How is this done? Use LaTex or Wolfram. Thanks.

    IMG_20220715_180149.jpg
     
    nycmathguy, Jul 15, 2022
    #1
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  2. nycmathguy

    MathLover1

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    upload_2022-7-15_17-29-39.gif

    first factor (x^5-a^5)

    upload_2022-7-15_17-30-25.gif

    then we have

    upload_2022-7-15_17-31-27.gif

    upload_2022-7-15_17-32-20.gif
     
    MathLover1, Jul 15, 2022
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  3. nycmathguy

    nycmathguy

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    nycmathguy, Jul 16, 2022
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  4. nycmathguy

    MathLover1

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    Apply factoring rule :
    x^n+y^n= (x+y ) (x^(n-1)-x^(n-2)y+...... -xy^(n-2)+y^(n-1)), where n is odd
     
    MathLover1, Jul 16, 2022
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  5. nycmathguy

    nycmathguy

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    I would like to see the factoring work, if you don't mind.
     
    nycmathguy, Jul 16, 2022
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  6. nycmathguy

    MathLover1

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    just apply rule and and use n=5

    x^5+a^5= (x+a ) (x^(5-1)a^(5-5) -x^(5-2)a^(5-4)+x^(5-3)a^(5-3)-x^(5-4)a^(5-2)+x^(5-5)a^(5-1))
    x^5+a^5= (x+a ) (x^4a^0 -x^3a^1+x^2a^2-x^1a^3+x^0a^4)
    x^5+a^5= (x+a ) (x^4 -x^3a+x^2a^2-xa^3+a^4)
     
    MathLover1, Jul 16, 2022
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  7. nycmathguy

    nycmathguy

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    Interestingly difficult.
     
    nycmathguy, Jul 17, 2022
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