a) (x² - 1) : (x - 1)
(x + 1)(x - 1) : (x - 1)
= x + 1
b) (x³ - 1) : (x - 1)
= (x - 1)(x² + x + 1) : (x - 1)
= x² + x + 1
c) (x⁴ - 1) : (x - 1)
= (x² + 1)(x² - 1)(x - 1)
= (x² + 1)(x + 1)(x - 1) : (x - 1)
= (x² + 1)(x + 1)
d) (x⁵⁰ - 1) : (x - 1)
= (x + 1)(x²⁴ - x²³ + x²² - x²¹ + x²⁰ - x¹⁹ + x¹⁸ - x¹⁷ + x¹⁶ - x¹⁵ + x¹⁴ - x¹³ + x¹² - x¹¹ + x¹⁰ - x⁹ + x⁸ - x⁷ + x⁶ - x⁵ + x⁴ - x³ + x² - x + 1)