Factorize $x^{3} - 2 x^{2} - x + 2$

(x + 1) (x + 2) (x - 1)

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(x + 1) (x - 2) (x - 1)

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(x + 2) (x - 2) (x - 1)

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None of these

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Solution

The correct option is D $((x + 1) (x - 2) (x - 1))$
Given $x^{3} - 2 x^{2} - x + 2$ is
Here, we write $- 2 x^{2} = - 3 x^{2} + x^{2}$ and $- x = - 3 x + 2 x$
$= x^{3} + x^{2} - 3 x^{2} - 3 x + 2 x + 2$
$= x^{2} (x + 1) - 3 x (x + 1) + 2 (x + 1)$
$= (x + 1) (x^{2} - 3 x + 2)$
$= (x + 1) (x^{2} - 2 x - x + 2)$
$= (x + 1) [x (x - 2) - 1 (x - 2)]$
$= (x + 1) (x - 2) (x - 1)$
Hence, the factors of the given expression are $(x + 1) (x - 2) (x - 1)$

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Similar questions

x^{3} - 2 x^{2} - x + 2

= (x - 1) (x - 2) (x + 1)

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

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

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x^{3} - 6 x^{2} + 11 x - 6

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