Question

Factorise: x^2 − 2x^2 − 2 x^2 − 2x − 3

Answer 1

Step-by-step explanation:

${x}^{3 } - {2x}^{2} - x + 2 \\ = {x}^{3} - x - {2x}^{2} + 2$

$grouping \: the \: {1}^{st} 2 \: term \: together \: and \: and \: the \: {2}^{nd} 2 \: together$

$= x( {x}^{2} - 1) - 2( {x}^{2} - 1)$

$=( {x}^{2} - 1)(x - 2)$

Using the identity:

${a}^{2} - {b}^{2} = (a + b)(a - b)$

$= ( {x}^{2} - {1}^{2} )(x - 2)$

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

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