What is factor 4x^{3/2}-13x^{1/2}-12x^{-1/2} ?

The solution to factor 4x^{3/2}-13x^{1/2}-12x^{-1/2} is ((4x+3)(x-4))/(x^{1/2)}

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factor 4x^{3/2}-13x^{1/2}-12x^{-1/2}

factor

4 x^{\frac{3}{2}} - 13 x^{\frac{1}{2}} - 12 x^{- \frac{1}{2}}

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

Solution steps

4 x^{\frac{3}{2}} - 13 x^{\frac{1}{2}} - 12 x^{- \frac{1}{2}}

Rewrite as

= 4 x^{\frac{3}{2}} - 13 x^{\frac{1}{2}} - 4 \cdot 3 x^{- \frac{1}{2}}

Factor out common term

4

= 4 (x^{\frac{3}{2}} - 3 x^{- \frac{1}{2}}) - 13 x^{\frac{1}{2}}

Factor

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

= - 13 x^{\frac{1}{2}} + 4 \cdot \frac{x ^{2} - 3}{x ^{\frac{1}{2}}}

Apply exponent rule:

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

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

= 4 x^{2} x^{- \frac{1}{2}} - 13 x^{1} x^{- \frac{1}{2}} - 12 x^{- \frac{1}{2}}

Factor out common term

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

= x^{- \frac{1}{2}} (4 x^{2} - 13 x - 12)

Factor

4 x^{2} - 13 x - 12 : (4 x + 3) (x - 4)

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

Refine

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

2 x^{3} y^{2} z + 10 x^{2} y z^{3}

- \frac{1}{3} \cdot 2

\frac{5}{6} x - \frac{1}{4} x \geq \frac{7}{12} x + \frac{2}{3}

7 x^{2} - 2 x - 5

\frac{6}{5 x ^{3} y} - \frac{1}{2 x ^{2} y ^{3}}

What is factor 4x^{3/2}-13x^{1/2}-12x^{-1/2} ?
The solution to factor 4x^{3/2}-13x^{1/2}-12x^{-1/2} is ((4x+3)(x-4))/(x^{1/2)}