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LCM of Polynomials

What 'is the ...

Question

What 'is the LCM of $x^{2} - 4$ and $x^{2} - 5 x + 6$ ?

(x - 2) (x + 2) (x - 3)

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(x - 2) (x + 2) (x + 3)

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(x + 3) (x - 3) (x + 2)

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(x - 2)^{2} (x - 3) (x + 4)

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Solution

The correct option is A $(x - 2) (x + 2) (x - 3)$
$x^{2} - 4 = (x)^{2} - (2)^{2}$
$= (x + 2) (x - 2)$
$x^{2} - 5 x + 6 = x^{2} - 3 x - 2 x + 6$
$= x (x - 3) - 2 (x - 3)$
$= (x - 3) (x - 2)$
$L . C . M . = (x - 2) (x + 2) (x - 3)$
Option A is correct.

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