Find the value

Question:

Find the value

$x^{2}+2 \sqrt{3} x-24$

 

Solution:

Splitting the middle term,

$=x^{2}+4 \sqrt{3} x-2 \sqrt{3} x-24$

$[\therefore 2 \sqrt{3}=4 \sqrt{3}-2 \sqrt{3}$ also $4 \sqrt{3}(-2 \sqrt{3})=-24]$

$=x(x+4 \sqrt{3})-2 \sqrt{3}(x+4 \sqrt{3})$

$=(x+4 \sqrt{3})(x-2 \sqrt{3})$

$\therefore x^{2}+2 \sqrt{3} x-24=(x+4 \sqrt{3})(x-2 \sqrt{3})$

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