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Factoring Question

  1. Mar 15, 2005 #1
    Hello All,

    Just trying to figure out how to factor the following problem.

    x^2 + 5 + 6/(x^2)

    Can anybody help me??

    Thanks
    P
     
  2. jcsd
  3. Mar 15, 2005 #2

    dextercioby

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    It's a biquadratic.You can make the substitution

    [tex] x^{2}=t [/tex]...It will be very simple then.Piut everything under a common denominator.

    Daniel.
     
  4. Mar 15, 2005 #3
    Kurt

    Thanks for the reply. Could you clarify this for me or expaned upon it.

    I am really confussed.

    Thanks
     
  5. Mar 15, 2005 #4
    Ok, you've got x^2 as your demonminator
     
  6. Mar 15, 2005 #5
    After you set the (x^2 +5 +6)/(x^2) equal to zero, mulitply both sides of the equation by x^2. That will eliminate your x^2 from the bottom of the equation. You should end up with

    x^2 + 11=0

    Then just complete the square and factor it.
     
  7. Mar 15, 2005 #6
    You'll get 11 when you simplify the 5+6 part of your equation.

    Does that help? :smile:
     
  8. Mar 15, 2005 #7

    dextercioby

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    It's actually

    [tex] \frac{x^{4}+5x^{2}+6}{x^{2}} [/tex]

    Daniel.
     
  9. Mar 15, 2005 #8
    It wouldn't be because if you multiply the left side of the equation with x^2 over one, the x^2's would divide out and you would be left with x^2 +11.
     
  10. Mar 15, 2005 #9

    dextercioby

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    [tex] x^{2}+5+\frac{6}{x^{2}}=\frac{x^{2}}{1}+\frac{5}{1}+\frac{6}{x^{2}}=\frac{x^{4}}{x^{2}}+\frac{5x^{2}}{x^{2}}+\frac{6}{x^{2}}=\frac{x^{4}+5x^{2}+6}{x^{2}} [/tex]

    Daniel.
     
  11. Mar 15, 2005 #10
    OK. Why are you two coming up with different answers?

    Kurt

    so would my factored answer be

    ((x^2+2)(x^2+3)) /x^2????
     
  12. Mar 15, 2005 #11
    Sorry Daniel thought your name was Kurt
     
  13. Mar 15, 2005 #12

    dextercioby

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    No problem.Exactly.Your answer is valid.:smile:

    Daniel.
     
  14. Mar 15, 2005 #13
    Is there anyway to check to see if this has been factored correctly?
     
  15. Mar 15, 2005 #14
    Thanks for your help and MissKittys
     
  16. Mar 15, 2005 #15
    I see where I went wrong. Sorry Daniel! :redface:

    I thought the x^2 +5 +6 was all in the numerator not x^2 +5 + (6/x^2).

    Thats why we were coming up with different answers. Your answer is correct. If you're not sure then try to FOIL it back into the quadratic it was before you factored it. :smile:
     
  17. Mar 15, 2005 #16
    No problem! Anytime. :smile:
     
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