What is factor 20x^{-1/2}+9x^{1/2}+x^{3/2} ?

The solution to factor 20x^{-1/2}+9x^{1/2}+x^{3/2} is ((x+4)(x+5))/(x^{1/2)}

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factor 20x^{-1/2}+9x^{1/2}+x^{3/2}

factor

20 x^{- \frac{1}{2}} + 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\frac{( x + 4 ) ( x + 5 )}{x ^{\frac{1}{2}}}

Solution steps

20 x^{- \frac{1}{2}} + 9 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}}

= 20 x^{- \frac{1}{2}} + 9 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}} (20 + 9 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}}

= 20 x^{- \frac{1}{2}} + 9 x^{1} x^{- \frac{1}{2}} + x^{2} x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (20 + 9 x + x^{2})

Factor

x^{2} + 9 x + 20 : (x + 4) (x + 5)

= x^{- \frac{1}{2}} (x + 4) (x + 5)

Refine

= \frac{( x + 4 ) ( x + 5 )}{x ^{\frac{1}{2}}}

x^{2} + 8 x + 1 = 10

\frac{79 + 7 i}{6 - 7 i}

x^{2} \cdot x^{- 2}

2 x + 1 < 5

\frac{2}{3} x^{2} - \frac{8}{3} x + 2 = 0

What is factor 20x^{-1/2}+9x^{1/2}+x^{3/2} ?
The solution to factor 20x^{-1/2}+9x^{1/2}+x^{3/2} is ((x+4)(x+5))/(x^{1/2)}