Question

How do you divide `(4 - x^2 + x^3) / (2 + x^2)`?

Answer 1

`=> x-1- (2x-6)/(x^2+2)`

Explanation:

Write as: `(x^3-x^2+0x+4)/(x^2+0x+2)`

I have added the place holder of `0x` to make the calculation formatting easier. It has no value.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`" "x^3-x^2+0x+4`
`color(magenta)(x)(x^2+0x+2) ->ul(x^3+0x^2+2x) larr" Subtract"`
`" "0-x^2-2x+4`
`color(magenta)(-1)(x^2+0x+2)->" " ul(-x^2-0x-2 ) larr" Subtract"`
`" "color(magenta)(0-2x+6 larr" Remainder")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`(x^3-x^2+0x+4)/(x^2+0x+2)" " =" " x-1+ (-2x+6)/(x^2+2)`

`=> x-1- (2x-6)/(x^2+2)`