What is factor 5x^{3/2}-15x^{1/2}+10x^{-1/2} ?

The solution to factor 5x^{3/2}-15x^{1/2}+10x^{-1/2} is 5(x^{3/2}-3x^{1/2}+2*1/(x^{1/2)})

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factor 5x^{3/2}-15x^{1/2}+10x^{-1/2}

factor

5 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}} + 10 x^{- \frac{1}{2}}

5 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 \cdot \frac{1}{x ^{\frac{1}{2}}})

Solution steps

5 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}} + 10 x^{- \frac{1}{2}}

Factor out common term

5 : 5 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 x^{- \frac{1}{2}})

= 5 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 x^{- \frac{1}{2}})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- \frac{1}{2}} = \frac{1}{x ^{\frac{1}{2}}}

= 5 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 \cdot \frac{1}{x ^{\frac{1}{2}}})

- 7 x - 8 = - 16

x y^{5} + x^{3} y^{3}

x^{2} - 12 x = - 32

2 x^{3} + 8 x^{2} + 10 x + 4

\frac{\frac{5 π}{3}}{2}

What is factor 5x^{3/2}-15x^{1/2}+10x^{-1/2} ?
The solution to factor 5x^{3/2}-15x^{1/2}+10x^{-1/2} is 5(x^{3/2}-3x^{1/2}+2*1/(x^{1/2)})