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Factorisation of Cubics

  1. Jan 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello there, hope you'r well.

    I am having trouble factorising this cubic. I am comfortable with quadratics however I have never had to factorise anything to the power 3 before.

    x^3+3x^2y+2xy^2+6y^3

    Thanks in advance for any input.

    Mike


    2. Relevant equations
    n/a


    3. The attempt at a solution
    I have had ago but didn't get very far!

    (3x+2y)(xy) that does the bit in the middle, excluding the two terms to the power 3.

    Thanks again for any help with this.

    Mike
     
  2. jcsd
  3. Jan 9, 2010 #2

    tiny-tim

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    Hi Mike! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Assuming it has rational roots, they must be x/y = ± 1 or 2 or 3 or 6, so just try all of them. :biggrin:

    (to save time, do the "odd" terms together, and the "even" terms together :wink:)
     
  4. Jan 9, 2010 #3

    LCKurtz

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    Try grouping the first two and last two terms together and factor each group. Then...
     
  5. Jan 9, 2010 #4
    Factor x2 from the first two terms and 2y2 from the last two terms.
     
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