Question

Given that (x-2) is a factor of (x³-8) ,what is the other factor?​

Answer 1

`x^2+2x+4`

Explanation:

This expression can also be written as a difference of cubes:

`x^3-2^3`

A important formula to remember is:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

We can use this to factor this expression:

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

Therefore the other factor is:

`x^2+2x+4`