Question

Factorize:
$6\sqrt{3}{x}^2-47x+5\sqrt{3}$

Answer 1

We have:
$6\sqrt{3}{x}^2-47x+5\sqrt{3}$
Now, we have to split ($-$47) into two numbers such that their sum is ($-$47) and their product is 90.
Clearly, $\left(-45\right)+\left(-2\right)=-47\mathrm{and}\left(-45\right)\times \left(-2\right)=90$.

$$\begin{gathered} \therefore 6\sqrt{3}{x}^2-47x+5\sqrt{3}=6\sqrt{3}{x}^2-2x-45x+5\sqrt{3} \\ =2x\left(3\sqrt{3}x-1\right)-5\sqrt{3}\left(3\sqrt{3}x-1\right) \\ =\left(3\sqrt{3}x-1\right)\left(2x-5\sqrt{3}\right) \end{gathered}$$