Need Help Factoring This Equation?

[powp]

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

 

[dextercioby]

It's a biquadratic.You can make the substitution

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

Daniel.

 

[powp]

Kurt

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

I am really confussed.

Thanks

 

[misskitty]

Ok, you've got x^2 as your demonminator

 

[misskitty]

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.

 

[misskitty]

You'll get 11 when you simplify the 5+6 part of your equation.

Does that help?

 

[dextercioby]

It's actually

$$\frac{x^{4}+5x^{2}+6}{x^{2}}$$

Daniel.

 

[misskitty]

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.

 

[dextercioby]

$$x^{2}+5+\frac{6}{x^{2}}=\frac{x^{2}}{1}+\frac{5}{1}+\frac{6}{x^{2}}=\frac{x^{4}}{x^{2}}+\frac{5x^{2}}{x^{2}}+\frac{6}{x^{2}}=\frac{x^{4}+5x^{2}+6}{x^{2}}$$

Daniel.

 

[powp]

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?

 

[powp]

Sorry Daniel thought your name was Kurt

 

[dextercioby]

No problem.Exactly.Your answer is valid.

Daniel.

 

[powp]

Is there anyway to check to see if this has been factored correctly?

 

[powp]

Thanks for your help and MissKittys

 

[misskitty]

I see where I went wrong. Sorry Daniel!

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.

 

[misskitty]

No problem! Anytime.