Divide:

x⁶ - 8 by x² - 2

(x⁶ - 8) ÷ (x² - 2)

= (x^2x3 - 2³) ÷ (x² - 2)

[Using the formula (a³ - b³) = (a - b)(a² + ab + b²)]

= [(x² - 2)(x⁴ + 2x² + 4)] ÷ (x² - 2)

= $\dfrac{\cancel{(x^2 - 2)}(x^4 + 2x^2 + 4)}{\cancel{(x^2 - 2)}}$

= (x⁴ + 2x² + 4)

Hence,(x⁶ - 8) ÷ (x² - 2) = (x⁴ + 2x² + 4)