# What is the result of dividing x^{3} - 6 by x + 2?

**Solution:**

( x^{3} - 6 )/(x + 2)

(x^{3} + 8 - 14)/(x + 2)

(x^{3} + 8 ) = (x)^{3} + (2)^{3}

We know from algebraic identities.

a^{3} + b^{3} = (a + b)(a² - ab + b²)

Therefore

(x)^{3} + (2)^{3} = (x + 2)(x² - 2x + 4)

Therefore x^{3} + 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 x^{3} - 6 by x + 2?

**Summary:**

The result of dividing x^{3} - 6 by x + 2 is quotient of x² - 2x + 4 and remainder -14

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