Question

How do you simplify `(8+x³) / (x+2)`?

Answer 1

Use the sum of cubes identity: `a^3+b^3 = (a+b)(a^2-ab+b^2)` to find:

`(8+x^3)/(x+2) = x^2-2x+4` with exclusion `x != -2`

Explanation:

`8+x^3 = x^3+2^3 = (x+2)(x^2-2x+4)`

So:

`(8+x^3)/(x+2) = ((x+2)(x^2-2x+4))/(x+2) = x^2-2x+4`

with exclusion `x != -2`