# Factoring with factorial exponents.

## Homework Statement

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

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.

Related Precalculus Mathematics Homework Help News on Phys.org
When you are normally factoring an expression, say $x^3+2x^2+x$, you factor the largest factor of each term out of the expression, in this case, the $x$, or $x^1$ (same thing): $x(x^2+2x+1)$. Can apply that same logic to the case when the exponent is negative, fractional, or both? Hint: What is the smallest degree of $x$ in the second expression you gave?

Last edited:
HallsofIvy
Homework Helper

## Homework Statement

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

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

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.

SammyS
Staff Emeritus