How do you factor the expression $4 x^{\frac{3}{2}} - 12 x^{\frac{1}{2}} + 8 x^{- \frac{1}{2}}$ $4x^(3/2) − 12x^(1/2) + 8x^(−1/2)$ ?

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How do you factor the expression $4 x^{\frac{3}{2}} - 12 x^{\frac{1}{2}} + 8 x^{- \frac{1}{2}}$ $4x^(3/2) − 12x^(1/2) + 8x^(−1/2)$ ?

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Answer 1 · 2016-02-19T18:10:13

I found: $\frac{4 (x - 1) (x - 2)}{\sqrt{x}}$ $(4(x-1)(x-2))/sqrt(x)$

Explanation:

I used the fact that:
$x^{\frac{a}{b}} = {\sqrt[b]{x}}^{a}$ $x^(a/b)=rootbx^a$
and
$x^{- a} = \frac{1}{x^{a}}$ $x^-a=1/x^a$
to get:
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How do you factor the expression $4 x^{\frac{3}{2}} - 12 x^{\frac{1}{2}} + 8 x^{- \frac{1}{2}}$ $4x^(3/2) − 12x^(1/2) + 8x^(−1/2)$ ?

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How do you factor the expression $4 x^{\frac{3}{2}} - 12 x^{\frac{1}{2}} + 8 x^{- \frac{1}{2}}$ $4x^(3/2) − 12x^(1/2) + 8x^(−1/2)$ ?