If the cubic equation $x^{3} - 10 x^{2} + 12 x + 72$ can be factorised into $(x + 2) . y^{2}$ , express $y$ in terms of $x$ .

x - 6

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x - 3

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x - 1

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x + 1

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Solution

The correct option is C $x - 6$
Given cubic expression is $x^{3} - 10 x^{2} + 12 x + 72$
$=$ $x^{3} + 2 x^{2} - 12 x^{2} - 24 x + 36 x + 72$
$=$ $x^{2} (x + 2) - 12 x (x + 2) + 36 (x + 2)$
$=$ $(x + 2) (x^{2} - 12 x + 36)$
$=$ $(x + 2) (x - 6)^{2}$
Then $(x + 2) y^{2} = (x + 2) (x - 6)^{2}$
$y = x - 6$

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