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Factorize:$x^2 - \sqrt{3}x - 6$
Given :
$x^2 - \sqrt{3}x - 6$
To do :
We have to factorize the given expression.
Solution :
$x^2 - \sqrt{3}x - 6=x^{2}-2 \sqrt{3} x+ \sqrt{3} x-6$ [Since $-2 \sqrt{3} x+\sqrt{3} x=- \sqrt{3} x$ and $-2 \sqrt{3} x\times\sqrt{3} x=-6\times x^2$]
$=x(x-2\sqrt{3})+ \sqrt{3}(x-2 \sqrt{3})$
$=(x-2 \sqrt{3})(x+\sqrt{3})$
Hence, $x^2 - \sqrt{3}x - 6=(x-2 \sqrt{3})(x+\sqrt{3})$.
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