Question

How do you divide `(x^2+x-2)/(2x + 4)` using polynomial long division?

Answer 1

`(x-1)/2`

Explanation:

`" "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.")`