Question

How do you divide `(x^4 - 16) /( x + 2)`?

Answer 1

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

Explanation:

Factorise `(x^4 - 16)` as it is the difference of 2 squares
You then get
`((x^2 - 4)(x^2 + 4))/(x + 2)`

`x^2 - 4` is also the difference of 2 squares and will factorise to `(x - 2)(x + 2)`
so this gives you `((x - 2)(x + 2)(x^2 +4))/(x + 2)`
The `(x + 2)` terms cancel out to give you
`(x - 2)(x^2 + 4)`