What is factor 8x^{-1/2}+6x^{1/2}+x^{3/2} ?

The solution to factor 8x^{-1/2}+6x^{1/2}+x^{3/2} is ((x+2)(x+4))/(x^{1/2)}

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factor 8x^{-1/2}+6x^{1/2}+x^{3/2}

factor

8 x^{- \frac{1}{2}} + 6 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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

Solution steps

8 x^{- \frac{1}{2}} + 6 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}}

= 8 x^{- \frac{1}{2}} + 6 x^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}} + x^{\frac{3}{2}}

Rewrite as

= 4 \cdot 2 x^{- \frac{1}{2}} + 3 \cdot 2 x^{- \frac{1}{2}} x^{2 \cdot \frac{1}{2}} + x^{\frac{3}{2}}

Factor out common term

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

= 2 x^{- \frac{1}{2}} (4 + 3 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}}

= 8 x^{- \frac{1}{2}} + 6 x^{1} x^{- \frac{1}{2}} + x^{2} x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (8 + 6 x + x^{2})

Factor

x^{2} + 6 x + 8 : (x + 2) (x + 4)

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

Refine

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

\frac{n}{6.5} = 16.6

- 1 < \frac{n}{2} + 1

3 x^{2} - 9 x + 4 = 0

- 2 \leq x \leq 4

3 k - 2 = 10

What is factor 8x^{-1/2}+6x^{1/2}+x^{3/2} ?
The solution to factor 8x^{-1/2}+6x^{1/2}+x^{3/2} is ((x+2)(x+4))/(x^{1/2)}