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Factoring determinant

  1. Jul 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Code (Text):

    | x       x^2   1  |
    | x^2      x    1  |
    | x^3    x^3   1  |
     
    The answer is = x^2(1-x)^2(1+2x)

    2. Relevant equations

    none

    3. The attempt at a solution
    By factoring the matrix step by step.

    Thanks :)
     
  2. jcsd
  3. Jul 24, 2008 #2

    Defennder

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    Homework Helper

    What's the problem here? Just use co-factor expansion along any row or column.
     
  4. Jul 24, 2008 #3
    Take advantage of the fact that you have a column of ones in the third column...

    [tex] \begin{vmatrix}
    x & x^2 & 1 \\
    x^2 & x & 1 \\
    x^3 & x^3 & 1
    \end{vmatrix}
    =
    \begin{vmatrix}
    x^2 & x \\
    x^3 & x^3
    \end{vmatrix} -
    \begin{vmatrix}
    x & x^2 \\
    x^3 & x^3
    \end{vmatrix} +
    \begin{vmatrix}
    x & x^2 \\
    x^2 & x
    \end{vmatrix}
    [/tex]

    So what does this end up being?
     
  5. Jul 24, 2008 #4
    Sorry for the question. I was confused by the question a moment ago because of language barrier.
     
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