Jamierox4ev3r one year ago More review! Help appreciated

1. Jamierox4ev3r

4e. Factor the following expression: $3x ^{\frac{ 3 }{ 2 }} -9x ^{\frac{ 1 }{ 2 }} +6x ^{-\frac{ 1 }{ 2 }}$

2. Jamierox4ev3r

I'm pretty lost on this, having to factor with the rational fractions is throwing me into a bit of a loop.

3. Jamierox4ev3r

Does anyone have a simple method of doing this by hand? Or do you recommend grabbing a calculator to look for x-intercepts so I can factor that way?

4. anonymous

hold on i gotta write it :)

5. Jamierox4ev3r

fair enough, thank you @PinkiePug

6. anonymous

$3(x \frac{ 1 }{ 2 } - 3x \frac{ 1 }{ 2 }+2 x \frac{ 1 }{ 2 }$ this is what i got

7. Astrophysics

$x^{1/2} \implies \sqrt{x}$ $x^{-1/2} \implies \frac{ 1 }{ \sqrt{x} }$ This may be easier to visualize, so we can write it as $3x^{3/2}-9\sqrt{x}+6\frac{ 1 }{ \sqrt{x} }$

8. Astrophysics

Then we can find the common denominator $\sqrt{x}$

9. Astrophysics

Your numerator should simplify into something better which you can factor

10. Jamierox4ev3r

Wait. so are you suggesting that we have to get rid of the negative exponents in order to successfully factor this?

11. phi

I would factor out 3x^-1/2 $3x ^{\frac{ 3 }{ 2 }} -9x ^{\frac{ 1 }{ 2 }} +6x ^{-\frac{ 1 }{ 2 }} \\ 3x ^{-\frac{ 1 }{ 2 }}\left( x^2 -3x +2\right)$

12. phi

now you can factor the quadratic

13. Astrophysics

Yeah that works to haha :P

14. Astrophysics

$\frac{ 3x^2-9x+6 }{ \sqrt{x} }$ is what you get from my suggestion

15. Jamierox4ev3r

oh. so i can factor $$x^{2}-3x+2$$, since that's the quadratic. Oh wow that's much simpler. So the final answer would be: $$3x^{-\Large\frac{1}{2}}$$(x-1)(x-2)

16. phi

yes, or put sqr(x) in the denominator it is still ugly. but it's factored

17. Jamierox4ev3r

so just so I know, for future problems like this, is it always acceptable to take out a value so that you're left with a quadratic that you can easily factor?

18. phi

it is a common trick. no guarantees, but something to try

19. Jamierox4ev3r

Fair enough. I'll keep that in mind. Thank you very much kind sir

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