Factoring Question

1. Mar 15, 2005

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

2. Mar 15, 2005

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.

3. Mar 15, 2005

powp

Kurt

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

I am really confussed.

Thanks

4. Mar 15, 2005

misskitty

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

5. Mar 15, 2005

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.

6. Mar 15, 2005

misskitty

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

Does that help?

7. Mar 15, 2005

dextercioby

It's actually

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

Daniel.

8. Mar 15, 2005

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.

9. Mar 15, 2005

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.

10. Mar 15, 2005

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????

11. Mar 15, 2005

powp

Sorry Daniel thought your name was Kurt

12. Mar 15, 2005

dextercioby

Daniel.

13. Mar 15, 2005

powp

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

14. Mar 15, 2005

powp

Thanks for your help and MissKittys

15. Mar 15, 2005

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.

16. Mar 15, 2005

misskitty

No problem! Anytime.