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Factorization of a complex polynomial

  1. Apr 23, 2012 #1
    1. The problem statement, all variables and given/known data
    p(x)=((x−1)^2 −2)^2 +3. From here find the full factorization of p(x) into the product of first order terms and identify all the
    complex roots.


    2. Relevant equations
    I am having trouble doing this by hand. I know there are four complex roots but can't seem to figure out how to get them factored out.


    3. The attempt at a solution
     
  2. jcsd
  3. Apr 23, 2012 #2

    SammyS

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    Solve [itex]\displaystyle ((x−1)^2 −2)^2 +3 = 0[/itex] in steps.

    First solve for [itex]\displaystyle ((x−1)^2 −2)\,.[/itex] There are two solutions.

    Then isolate [itex]\displaystyle (x−1)^2[/itex] for each of the above solutions and take the square root of both sides in each case.
     
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