Question

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

Answer 1

We have:
$\sqrt{5}{x}^2+2x-3\sqrt{5}$
We have to split 2 into two numbers such that their sum is 2 and product is ($-$15), i.e.,$\sqrt{5}\times \left(-3\sqrt{5}\right)$.
Clearly, $5+\left(-3\right)=2\mathrm{and}5\times \left(-3\right)=-15$.

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