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Expansion of (x^2 - y^2)

Factorise: ...

Question

Factorise: $x^{3} - 6 x^{2} + 11 x - 6$

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Solution

$x^{3} - 6 x^{2} + 11 x - 6$
$= x^{3} - 5 x^{2} - x^{2} + 6 x + 5 x - 6$
$= x^{3} - 5 x^{2} + 6 x - x^{2} + 5 x - 6$
$= x (x^{2} - 5 x + 6) - 1 (x^{2} - 5 x + 6)$
$= (x - 1) (x^{2} - 5 x + 6)$
$= (x - 1) (x^{2} - 2 x - 3 x + 6)$
$= (x - 1) [x (x - 2) - 3 (x - 2)]$
$= (x - 1) (x - 2) (x - 3)$

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

Q. Factorise the expression

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Q. using the factor theorem factorise the following

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

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