LCM of $x^{2} + x - 6$ and $(x - 2)^{2}$ is $(x + a)$ $(x - b)^{2}$ . Value of $(a + b)^{2}$ =

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Solution

The correct option is B
25

First expression, $x^{2} + x - 6$ can be factorized as $(x - 2) (x + 3)$ .

Second expression, $(x - 2)^{2}$ can be factorized as $(x - 2) (x - 2)$ .

So, the LCM of both the expressions = $(x + 3)$ $(x - 2)^{2}$

Hence, $a = 3, b = 2$

$∴ (a + b)^{2} = (3 + 2)^{2} = 25$

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