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