Factoring with factorial exponents.

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Homework Help Overview

The discussion revolves around factoring expressions that involve negative and fractional exponents, specifically focusing on the expressions x + 5 + 6x^-1 and x^(3/2) + 2x^(1/2) - 8x^(-1/2). Participants are exploring how to approach factoring in this context, particularly as it relates to a review before calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants discuss the method of factoring out the smallest degree of x from the expressions. Others question whether the same factoring logic applies to negative and fractional exponents as it does to positive integers.

Discussion Status

Participants are actively engaging with the problem, with some offering guidance on how to factor the expressions by identifying common factors. There is a recognition of the challenge posed by the negative and fractional exponents, and the discussion is ongoing without a clear consensus on the best approach.

Contextual Notes

One participant notes that the expressions involve fractional exponents, clarifying a potential misunderstanding regarding the term "factorial exponents." This highlights the need for clarity in terminology as the discussion progresses.

ponyberry
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Homework Statement



Factor x + 5+ 6x^-1
Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2)

Homework Equations



None given.

The Attempt at a Solution



I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math class before, but my teacher is doing this as part of a review before calculus. If someone could show me what I need to do, I would really appreciate it and would be able to apply it to the rest of the worksheet.
 
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When you are normally factoring an expression, say [itex]x^3+2x^2+x[/itex], you factor the largest factor of each term out of the expression, in this case, the [itex]x[/itex], or [itex]x^1[/itex] (same thing): [itex]x(x^2+2x+1)[/itex]. Can apply that same logic to the case when the exponent is negative, fractional, or both? Hint: What is the smallest degree of [itex]x[/itex] in the second expression you gave?
 
Last edited:
ponyberry said:

Homework Statement



Factor x + 5+ 6x^-1
The very first thing you could do is factor out [itex]x^{-1}[/itex] giving
[itex]x^{-1}(x^2+ 5x+ 6)[/itex]. Can you continue that?

Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2)
If you factor out [itex]x^{-1/2}[/itex] you get [itex]x^{-1/2}(x^2+ 2x- 8)[/itex]

Homework Equations



None given.

The Attempt at a Solution



I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math class before, but my teacher is doing this as part of a review before calculus. If someone could show me what I need to do, I would really appreciate it and would be able to apply it to the rest of the worksheet.
 
Those are fractional exponents, not factorial exponents.
 

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