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

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

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Answer 1 · 2016-10-01T12:38:56

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

Explanation:

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

$g (x) \div f (x) = \frac{2 x^{2} - 4 x + 2}{x + 2} \leftarrow$ $color(red)(g(x))÷color(blue)(f(x)) = color(red)(2x^2-4x+2)/color(blue)(x +2)" "larr$ simplify as normal

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

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

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

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

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Given f(x)=x+2f(x) = x +2 and g(x)=2x2−4x+2g(x)= 2x^2-4x+2, how do you find g(x)÷f(x)g(x)÷f(x)?

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