Factorize: 8/27x^3 + 1 + 4/3x^2 + 2x

Question

Factorize:

\(\frac{8}{27}\)x³ + 1 + \(\frac{4}{3}\)x² + 2x

Answer 1

Given,

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

= \((\frac{2}{3}\text{x})^{3}+(1)^3+2\text{x}(\frac{2}{3}\text{x}+1)\)

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

= \((\frac{2}{3}\text{x}\,+1)^3\)

= \((\frac{2}{3}\text{x}\,+1)(\frac{2}{3}\text{x}+1)(\frac{2}{3}\text{x}+1)\)