Factoring with factorial exponents.

[ponyberry]

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.

 

[Accretion]

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?

 

[HallsofIvy]

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 $x^{-1/2}(x^2+ 2x- 8)$

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.

 

[SammyS]

Those are fractional exponents, not factorial exponents.