Respuesta:
[tex]x - 2[/tex]
Explicación paso a paso:
[tex](x {}^{3}- x { }^{2} - x - 2) \div (x {}^{2} + x + 1) = \\ \frac{ \times {}^{3} - \times {}^{2} - x - 2}{ \times {}^{2} + x + 1} = \\ \frac{x {}^{3} - 2x {}^{2} + x {}^{2} - 2x + x - 2 }{x {}^{2} + x + 1} = \\ \frac{x {}^{2} \times (x - 2) + x \times (x - 2) + 1(x - 2) }{x {}^{2} + x + 1 } = \\ \frac{(x - 2) \times ( \times {}^{2} + x + 1)} { \times {}^{2} + x + 1} = \\ x - 2[/tex]
