Question

$x \: cube + 2x \: cube - x - 2$
Factorise

Answer 1

Hope u like my process
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Here you have a simple mistake on the question of writing cube in place of square.

Thus I am correcting the question and providing u with the answer.
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The required factorization for
=> x³ +2x² - x - 2. is

= > x³ + 2x² - x - 2

= x³ + x² +x² +x - 2x - 2

= x²(x +1) +x(x +1) - 2(x+1)

= (x +1)(x² +x - 2)

= (x +1)(x² + 2x - x - 2)

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

= (x +1)(x-1)(x+2)
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Alternative way
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=> x³ +2x² - x - 2

= x²(x +2) - 1(x +2)

= (x² - 1)(x +2)

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

_[since, (x² - 1) = (x-1)(x+1)]__

So the required factorization is

$= > \boxed{ \underline{ \bold{( \green{x - 1})( \green{x + 1})( \green{x + 2})}}}$
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Hope this is ur required answer

Proud to Help you.