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

1 Answer
Oct 1, 2016

$= \frac{2 \left(x - 1\right) \left(x - 1\right)}{x + 2}$

Explanation:

$\textcolor{b l u e}{f \left(x\right) = x + 2} \text{ }$ and $\text{ } \textcolor{red}{g \left(x\right) = 2 {x}^{2} - 4 x + 2}$

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

$= \frac{2 \left({x}^{2} - 2 x + 1\right)}{x + 2}$

$= \frac{2 \left(x - 1\right) \left(x - 1\right)}{x + 2}$

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