How to factor $$3x^{\frac{3}{2}} - 9x^{\frac{1}{2}} + 6x^{\frac{-1}{2}}$$

Question

anonymous · Answer

rfresh it

parthkohli · Answer

Convert them into improper fractions first.

anonymous · Answer

improper fractions?

parthkohli · Answer

$\Large \color{purple}{\rightarrow a{b \over c} = {ac + b \over c} }$

callisto · Answer

$$3x^{\frac{3}{2}}-9x^{\frac{1}{2}}+6x^{-\frac{1}{2}}$$$$=3x^{-\frac{1}{2}}(x^{\frac{3}{2}+\frac{1}{2}}-3x^{\frac{1}{2}+\frac{1}{2}}+2)$$$$=3x^{-\frac{1}{2}}(x^2-3x+2)$$$$=3x^{-\frac{1}{2}}(x-2)(x-1)$$

parthkohli · Answer

Oh wait, these were exponents?

anonymous · Answer

i dont get what @Callisto did either :/

callisto · Answer

Take out x^{-1/2} as a common factor, then factorise it

anonymous · Answer

uhmm can we like use quadratics or something? i dont know..you're better at me with this :(

callisto · Answer

Quadratic? yes when you factorise (x^2 -3x +2)
But do it by factoring the expression is easier... and answer is trivial :|

anonymous · Answer

i can see :/ pls guide me

callisto · Answer

if you can see, why need I guide? (no offense...)

anonymous · Answer

lol :p i can see what you mean but i dont know how to do this

callisto · Answer

.... Sorry..
x^2 -3x +2 = x^2 -2x -x +2 = x(x-2) - (x-2) = (x-1)(x-2)

anonymous · Answer

now you're just confusing me

anonymous · Answer

how did you get that x^2- 3x + 2 again?

callisto · Answer

......
Please refer to the second step.

anonymous · Answer

but how do you know what exponent to factor out? i mean is there a way to know?

callisto · Answer

Finding the HCF of the terms...

anonymous · Answer

i always get confused with factoring fractional exponents sorry @FoolForMath

anonymous · Answer

ohhhh it's x^3/2 - (-1/2) that right?

callisto · Answer

The problem is the HCF in this case is 3x^{-1/2}

callisto · Answer

x^[3/2 - (-1/2) ]
is for the first term

anonymous · Answer

oohhh ok...carry on..so we do qaudratics?

callisto · Answer

Why quadratic?

anonymous · Answer

i dont know..you said we do after factoring

callisto · Answer

......
You were asking factorization.. So I did factorization.
Using quadratic (formula) to do factorization is kind of cheating, though  you can use it.

callisto · Answer

Welcome

anonymous · Answer

o_o iss it me or did your smartscore just shoot up? xD

anonymous · Answer

haha