Factors of polynomial with fractional powers

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Homework Help Overview

The discussion revolves around the factorization of the polynomial a^{3/2}+x^{3/2}, specifically focusing on the challenges posed by fractional powers in polynomial expressions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the possibility of factorization, with one suggesting that (√x + √a) could be a factor. Others discuss methods like polynomial division and substitutions to aid in the factorization process.

Discussion Status

The conversation includes various approaches to factorization, with some participants sharing insights and others reflecting on their understanding of the topic. There is an indication of progress as one participant mentions figuring out a solution independently.

Contextual Notes

Participants express a need to refresh their mathematical skills, indicating a potential gap in recent practice with polynomial concepts and operations involving fractional powers.

hustler
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Hi,
I've got this particular polynomial [tex]a^{3/2}+x^{3/2}[/tex] and I need to factorize it as far as possible.
I've come to the conclusion that there are no factors.
Am I wrong?
 
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(x + a) isn't a factor, but (√x + √a) is.
 
Ok, that seems straightforward, but how do I go about doing polynomial division using fractional powers to find the polynomial remainder?
Actually, nevermind. I just figured it out. Thanks for the help.
 
Set [itex]x = y^2[/itex] and [itex]b = a^2[/itex] then see if anything comes to mind! :)
 
Yeah, that's what I figured out.
Haven't done any mathematics for a long time. Need to get the gray cells into action.
 

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