Question

How do you divide `(-2x^3-16x^2+13x-40)/(x-3)`?

Answer 1

`-2x^2-22x-53-199/(x-3)`

Explanation:

`" "-2x^3-16x^2+13x-40`
`color(red)(-2x^2)(x-3)->" "ul(-2x^3+6x^2) larr" subtract"`
`" "0-22x^2+13x-40`
`color(red)(-22x)(x-3)->" "ul(-22x^2+66x) larr" subtract"`
`" "0-53x-40`
`color(red)(-53)(x-3)-> " "ul(-53x+159) larr" subtract"`
`" "0color(red)(-199 larr" remainder")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(red)(-2x^2-22x-53-199/(x-3))`