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Factorize:$x^2 + 2\sqrt{3}x - 24$
Given :
$x^2 + 2\sqrt{3}x - 24$
To do :
We have to factorize the given expression.
Solution :
$x^2 +2 \sqrt{3}x - 24=x^{2}+4 \sqrt{3} x- 2\sqrt{3} x-24$ [Since $4\sqrt{3} x-2\sqrt{3} x=2\sqrt{3} x$ and $4 \sqrt{3} x\times-2\sqrt{3} x=-24\times x^2$]
$=x(x+4\sqrt{3})- 2\sqrt{3}(x+4\sqrt{3})$
$=(x+4 \sqrt{3})(x-2\sqrt{3})$
Hence, $x^2 +2 \sqrt{3}x - 24=(x+4 \sqrt{3})(x-2\sqrt{3})$.
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