Question

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

Answer 1

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

Here, we need to seclect two terms such that, their sum is $2\sqrt{3}$[since, middle term is $2\sqrt{3}x$] and their product is $-24x^2$. [Since, $x^2\times (-24)=-24x^2$].

Clearly, $+4\sqrt{3}x-2\sqrt{3}x=+2\sqrt{3}x$ and $(+4\sqrt{3}x)\times \left(2\sqrt{3}x\right)=-24x^2$

Now, lets do factorisation,

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

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

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

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

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

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