Question

Разложите на множители: x⁸+x⁷+1

Answer 1

x⁸ + x⁷ + 1 = x⁸ + x⁷ + x⁶ - x⁶ + 1 = (x⁸ + x⁷ + x⁶) - (x⁶ - 1) =

= x⁶(x² + x + 1) - ((x³)² - 1) = x⁶(x² + x + 1) - (x³ - 1)(x³ + 1) =

= x⁶(x² + x + 1) - (x - 1)(x² + x + 1)(x³ + 1) = (x² + x + 1)(x⁶ - x⁴ + x³ - x + 1)