Factorise : $x^{3}-2 x^{2}-x+2$
Factorise : $x^{3}-2 x^{2}-x+2$
$x^{3}-2 x^{2}-x+2$
Rearranging the terms, we have
$x^{3}-2 x^{2}-x+2=x^{3}-x-2 x^{2}+2=x\left(x^{2}-1\right)-2\left(x^{2}-1\right)$
$=\left(x^{2}-1\right)(x-2)$
$=\left[(x)^{2}-(1)^{2}\right][x-2]$
$=(x-1)(x+1)(x-2)$
$\left[\because a ^{2}- b ^{2}=( a + b )( a - b )\right]$
Thus, $x^{3}-2 x^{2}-x+2=(x-1)(x+1)(x-2)$
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