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Homework Help: Factors of a polynomial

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that every polynomial with real coefficients factors into linear and quadratic real factors.

    2. Relevant equations
    So show that f(x) = x[tex]^{n}[/tex] + a[tex]_{}n-1[/tex]x[tex]^{n-1}[/tex]+...+ax +a[tex]_{}0[/tex] factors into some (x-r[tex]_{}1[/tex])(x[tex]^{2}[/tex]+4)......

    3. The attempt at a solution
    I understand how and why this is true but could someone point me in the right direction on where to start?
    Last edited: Oct 16, 2008
  2. jcsd
  3. Oct 16, 2008 #2


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    Science Advisor
    Homework Helper

    If all of the roots r_i are real then you are done. Suppose there is a factor (x-a) with 'a' complex? You can match that up with another factor so that the product is a real quadratic. What's that other factor and how do you know it exists?
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