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Factorizing with no GCF

  1. Jan 12, 2008 #1
    Hi all,

    I was hoping someone could help me with factorizing an expression that has no common factors. I'm working through some pre-module work and I've never come across them before and have no idea where to start!

    They are all in the format:

    x^2 - ax - b (where there are no common factors for x, a and b)

    All I know is that when there are no common factors the GCF is 1, but thats about it :(
    Any help or good places to look to get me started are much appreciated.

    Many thanks in advance,

    Theinvoker :)
  2. jcsd
  3. Jan 12, 2008 #2


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    Homework Helper

    if x_1 and x_2 are zeroes to your expression x^2 - ax - b , then

    x^2 - ax - b = (x-x_1)*(x-x_2)
  4. Jan 12, 2008 #3
    Thanks for the quick reply. Im still a bit lost tho :(

    As an example:

    x^2 + 24x +133

    I can see the answer is (x + sqrt11+12)(x - sqrt11+12) by using my calculator but cant figure out how to get there.

    Many thanks again!
  5. Jan 12, 2008 #4


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    For the quadratic equation [itex]ax^2+bx+c=0[/itex]

    [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
  6. Jan 12, 2008 #5
    Ok now I feel like a right idiot lol. Many thanks couldnt see the wood for the trees! :)
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