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Solution:
( x3 - 6 )/(x + 2)
(x3 + 8 - 14)/(x + 2)
(x3 + 8 ) = (x)3 + (2)3
We know from algebraic identities.
a3 + b3 = (a + b)(a² - ab + b²)
Therefore
(x)3 + (2)3 = (x + 2)(x² - 2x + 4)
Therefore x3 + 8 - 14 when divided by (x + 2) will give
(x² - 2x + 4) as quotient and leave -14 as remainder.
Summary:
The result of dividing x3 - 6 by x + 2 is quotient of x² - 2x + 4 and remainder -14