Given,
\(\frac{8}{24}\text{x}^3+1+\frac{4}{3}\text{x}^2\,+2\text{x},\)
= \((\frac{2}{3}\text{x})^{3}+(1)^3+2\text{x}(\frac{2}{3}\text{x}+1)\)
= \((\frac{2}{3}\text{x})^3+(1)^3+3\text{x}\frac{2}{3}\text{x}\,\times1(\frac{2}{3}\text{x}+1)\)
= \((\frac{2}{3}\text{x}\,+1)^3\)
= \((\frac{2}{3}\text{x}\,+1)(\frac{2}{3}\text{x}+1)(\frac{2}{3}\text{x}+1)\)