Question

Factorize:
$7\sqrt{2}{x}^3-10x-4\sqrt{2}$

Answer 1

We have:
$7\sqrt{2}{x}^2-10x-4\sqrt{2}$
We have to split ($-$10) into two numbers such that their sum is ($-$10) and their product is ($-$56), i.e., $7\sqrt{2}\times \left(-4\sqrt{2}\right)=-28\times 2$.
Clearly, $-14+4=-10\mathrm{and}-14\times 4=-56$.

$$\begin{gathered} \therefore 7\sqrt{2}{x}^2-10x-4\sqrt{2}=7\sqrt{2}{x}^2-14x+4x-4\sqrt{2} \\ =7\sqrt{2}x\left(x-\sqrt{2}\right)+4\left(x-\sqrt{2}\right) \\ =\left(x-\sqrt{2}\right)\left(7\sqrt{2}x+4\right) \end{gathered}$$