Question

How do you divide `(2x^2+4x-4)div(x-2)` using synthetic division?

Answer 1

The answer is `(2x^2+4x-4)/(x-2)=2x+8+12/(x-2)`

Explanation:

Let's do the long division
`2x^2+4x-4` `color(white)(aaaaa)` `∣` `x-2`
`2x^2-4x` `color(white)(aaaaaaaaa)` `∣` `2x+8`
`color(white)(aa)` `0+8x-4`
`color(white)(aa)` `0+8x-16`
`color(white)(aaaaaa)` `0+12`

So `(2x^2+4x-4)/(x-2)=2x+8+12/(x-2)`

The remainder can be obtained
let `f(x)=2x^2+4x-4`
then `f(2)=2*2^2+4*2-4=12`