X^3/2 - 2x^-1/2 + x^1/2 Help Factoring

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In summary, the conversation involves a person asking for help in factoring an equation and mentioning that they got the answer 1-x^4/3 but are unsure how to obtain it. They also mention trying to factor x^-3/2 and ask for clarification on how to do so. Another person suggests using substitution and the original person realizes they made a mistake and apologizes. They also mention posting in the wrong section and feeling fatigued.
  • #1
Hierophant
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I'm looking to factor this...


X^3/2 - 2x^-1/2 + x^1/2

The textbook offers the solution 1-x ^4/3

No idea how to get this result. I got X ^-3/2 (x-1)^2
I would like it if someone could shed light on how to factor x^-3/2 from things like 2x ^1/2
I assume you just keep the equation balance, so if you re-distribute everything, it reverts to the original.

I would like to know how you get the answer too.

Thanks so much!
 
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  • #2
Maybe you can do substitution, say ##u = x^{1/2}##?
 
  • #3
Hierophant said:
I'm looking to factor this... X^3/2 - 2x^-1/2 + x^1/2

The textbook offers the solution 1-x ^4/3

No idea how to get this result. I got X ^-3/2 (x-1)^2

Both look wrong
Mod note: Removed complete answers.
 
Last edited by a moderator:
  • #4
Hierophant said:
I'm looking to factor this...

X^3/2 - 2x^-1/2 + x^1/2

The textbook offers the solution 1-x ^4/3

No idea how to get this result. I got X ^-3/2 (x-1)^2
I would like it if someone could shed light on how to factor x^-3/2 from things like 2x ^1/2
I assume you just keep the equation balance, so if you re-distribute everything, it reverts to the original.

I would like to know how you get the answer too.

Thanks so much!

So why are you looking to factor this, what exactly are you trying to obtain?

Also this should go in homework help, fyi.

edit:
Pwan just gave your answer, but is this what you're even looking for?
 
Last edited:
  • #5
To my delight and perhaps also not to my delight, I got the correct answer, but used the wrong answer key. Sorry guys, won`t happen again.

Also sorry for posting in the wrong section, I was rather fatigued at the moment of posting.

I`m just going to go sit in the corner now.
 
  • #6
To my delight and perhaps also not to my delight, I got the correct answer, but used the wrong answer key. Sorry guys, won`t happen again.

Also sorry for posting in the wrong section, I was rather fatigued at the moment of posting.

I`m just going to go sit in the corner now.
 

1. What is the formula for factoring X^3/2 - 2x^-1/2 + x^1/2?

The formula for factoring X^3/2 - 2x^-1/2 + x^1/2 is (x^-1/2)(x^2 - 2 + x).

2. How do you factor X^3/2 - 2x^-1/2 + x^1/2 by grouping?

To factor X^3/2 - 2x^-1/2 + x^1/2 by grouping, we first group the first two terms together and the last two terms together. This gives us (x^-1/2)(x^2 - 2) + (x^-1/2)(x). We then factor out the common factor of x^-1/2 from each group, giving us (x^-1/2)(x(x - 2) + 1). Finally, we factor the expression inside the parentheses to get the final factored form of (x^-1/2)(x - 1)^2.

3. Can X^3/2 - 2x^-1/2 + x^1/2 be factored using the difference of squares formula?

No, X^3/2 - 2x^-1/2 + x^1/2 cannot be factored using the difference of squares formula because it does not have the form of a^2 - b^2.

4. Is there a way to factor X^3/2 - 2x^-1/2 + x^1/2 without using grouping?

Yes, X^3/2 - 2x^-1/2 + x^1/2 can also be factored by recognizing that it is a perfect square trinomial. The factored form is (x^-1/2 - 1)^2.

5. Can X^3/2 - 2x^-1/2 + x^1/2 be factored using the quadratic formula?

No, X^3/2 - 2x^-1/2 + x^1/2 cannot be factored using the quadratic formula because it is not a quadratic equation. The highest degree of the variable is 3/2, which is not a whole number.

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