Question

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

Answer 1

`-x^2+2x+9+24/(x-3)`

Explanation:

`color(green)(color(white)("dddddddddddd")-x^3-x^2+3x-3)`
`color(green)(color(red)(-x^2)(x-3)-> ul(-x^2-3x^2 larr" Subtract"))`
`color(green)(color(white)("ddddddddddddd.d")0+2x^2+3x-3)`
`color(green)(color(red)(+2x)(x-3)-> color(white)("dddd..d")ul(2x^2-6xlarr" Subtract"))`
`color(green)(color(white)("ddddddddddddddddddd")0color(white)(".")+9x-3)`
`color(green)(color(red)(+9)(x-3)-> color(white)("ddd.dddddd..d")ul(9x-27larr" Subtract"))`
`color(red)("remainder"->color(white)("dddddddddddd")0color(white)("d")+24)`

`color(red)( -x^2+2x+9+24/(x-3)`