Question

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

Answer 1

`-x^2-4x-9 -31/(x-3)`

Explanation:

Given: `(-x^3-x^2+3x-4)/(x-3)`

`color(white)("ddddddddddddd") -x^3-x^2+3x-4`
`color(red)(-x^2)(x-3) ->color(white)("d") ul(-x^3+3x^2 larr" Subtract")`
`color(white)("ddddddddddddddd")0-4x^2+3x-4`
`color(red)(-4x)(x-3) -> color(white)("ddd.d")ul(-4x^2+12xlarr" Subtract" )`
`color(white)("ddddddddddddddddddd")0 color(white)("d.")-9x-4`
`color(red)(-9)(x-3)->color(white)("ddddddddddd")ul( -9x+27larr" Subtract")`
`color(red)("Remainder" ->color(white)("dddddddddddd")0color(white)("d")-31`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(red)(-x^2-4x-9 -31/(x-3))`