Question

How do I use long division to simplify `(2x^3-4x+7x^2+7)/(x^2+2x-1)`?

Answer 1

`(2x+3)` with remainder of `(-8x+10)`

Explanation:

First arrange the dividend into order of descending powers of `x`
`color(white)("XXX")2x^3+7x^2-4x+7`

Long Polynomial Division:
`{: (,,,,2x,+3,,), (,,,,"----","----","---","----"), (x^2,+2x,-1,")",2x^3,+7x^2,-4x,+7), (,,,,2x^3,+4x^2,-2x,), (,,,,"----","----","----","----"), (,,,,,3x^2,-2x,+7), (,,,,,3x^2,+6x,-3), (,,,,,"----","----","----"), (,,,,,,-8x,+10) :}`