What is the result of dividing x³ - 6 by x + 2?

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.

What is the result of dividing x³ - 6 by x + 2?

Summary:

The result of dividing x³ - 6 by x + 2 is quotient of x² - 2x + 4 and remainder -14