Question

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

Answer 1

We have to split 3root3 into two numbers such that their sum is $3root3$ and their product is 6, i.e.,$2\times 3$.

Clearly, $2\sqrt{3}+\sqrt{3}=3\sqrt{3}$ and $2\sqrt{3}\times \sqrt{3}=6.$

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