What is factor 15x^{-1/2}+8x^{1/2}+x^{3/2} ?

The solution to factor 15x^{-1/2}+8x^{1/2}+x^{3/2} is ((x+3)(x+5))/(x^{1/2)}

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factor 15x^{-1/2}+8x^{1/2}+x^{3/2}

factor

15 x^{- \frac{1}{2}} + 8 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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

Solution steps

15 x^{- \frac{1}{2}} + 8 x^{\frac{1}{2}} + x^{\frac{3}{2}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

= 15 x^{- \frac{1}{2}} + 8 x^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}} + x^{\frac{3}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (15 + 8 x^{2 \cdot \frac{1}{2}}) + x^{\frac{3}{2}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{\frac{1}{2}} = x^{1 +- \frac{1}{2}} = x^{1} x^{- \frac{1}{2}}, x^{\frac{3}{2}} = x^{2 +- \frac{1}{2}} = x^{2} x^{- \frac{1}{2}}

= 15 x^{- \frac{1}{2}} + 8 x^{1} x^{- \frac{1}{2}} + x^{2} x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (15 + 8 x + x^{2})

Factor

x^{2} + 8 x + 15 : (x + 3) (x + 5)

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

Refine

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

x - 4 = - 1

1 + 3 u \leq 10

- 2 x + 5 \leq 11

\frac{1}{100} e^{- 10 \cdot 0.5}

(- 5 x^{2} y^{3})^{2}

What is factor 15x^{-1/2}+8x^{1/2}+x^{3/2} ?
The solution to factor 15x^{-1/2}+8x^{1/2}+x^{3/2} is ((x+3)(x+5))/(x^{1/2)}