2) 3x³ + x² – 3x – 1, если x = 2\frac{2}{3};

Решение:

\(3x^3 + x^2 - 3x - 1 = (3x^3 - 3x) + (x^2 - 1) = 3x(x^2 - 1) + (x^2 - 1) = (3x + 1)(x^2 - 1) = (3x + 1)(x - 1)(x + 1)\) Подставим \(x = 2\frac{2}{3} = \frac{8}{3}\): \((3 \cdot \frac{8}{3} + 1)(\frac{8}{3} - 1)(\frac{8}{3} + 1) = (8 + 1)(\frac{8}{3} - \frac{3}{3})(\frac{8}{3} + \frac{3}{3}) = 9 \cdot \frac{5}{3} \cdot \frac{11}{3} = \frac{495}{9} = \frac{165}{3} = 55\)