How do you divide $\frac{x^{2} + x - 2}{2 x + 4}$ $(x^2+x-2)/(2x + 4)$ using polynomial long division?

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How do you divide $\frac{x^{2} + x - 2}{2 x + 4}$ $(x^2+x-2)/(2x + 4)$ using polynomial long division?

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Answer 1 · 2017-04-05T13:37:19

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

Explanation:

$x^{2} + x - 2$ $" "x^2+x-2$
$color(magenta)(1/2x)(2x+4)->" "ul(x^2+2x) larr" subtract"$
$" "0 -x-2$
$color(magenta)(-1/2)(2x+4)->" "ul( -x-2) larr" subtract"$
$" "0+0 larr" remainder"$

As the remainder is zero the division is exact.

$(x^2+x-2)/(2x+4)=color(magenta)( x/2-1/2)->(x-1)/2$

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$color(brown)("The above is actually the same process as the traditional method.")$ $color(brown)("The only difference is the format chosen.")$

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How do you divide $\frac{x^{2} + x - 2}{2 x + 4}$ $(x^2+x-2)/(2x + 4)$ using polynomial long division?

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How do you divide $\frac{x^{2} + x - 2}{2 x + 4}$ $(x^2+x-2)/(2x + 4)$ using polynomial long division?