Question

Given `f(x) = x +2` and `g(x)= 2x^2-4x+2`, how do you find `g(x)÷f(x)`?

Answer 1

`=(2(x-1)(x-1))/(x +2)`

Explanation:

`color(blue)(f(x) = x +2)" "` and `" "color(red)(g(x)= 2x^2-4x+2)`

`color(red)(g(x))÷color(blue)(f(x)) = color(red)(2x^2-4x+2)/color(blue)(x +2)" "larr` simplify as normal

`=(2(x^2-2x+1))/(x +2)`

`=(2(x-1)(x-1))/(x +2)`

(You could do the division by long/synthetic division, but I do not believe there is any advantage in doing so)