Factorize: `3x^(3/2) -9x^(1/2) + 6x^(-1/2)`

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justaguide eNotes educator| Certified Educator

The factorized form of `3x^(3/2) -9x^(1/2) + 6x^(-1/2)` has to be determined

`3x^(3/2) -9x^(1/2) + 6x^(-1/2)`

=> `3*x^(1/2)*(x - 3 + 2/x)`

=> `(3/sqrt x)*(x^2 - 3x + 2)`

=> `(3/sqrt x)*(x^2 - 2x - x + 2)`

=> `(3/sqrt x)*(x(x - 2) - 1(x - 2))`

=> `(3/sqrt x)*(x - 1)(x - 2)`

The factorized form of `3x^(3/2) -9x^(1/2) + 6x^(-1/2)` = `(3*(x - 1)(x - 2))/sqrt x`

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