Question

How do you divide `(-2x^3+7x^2-4x-1)/(3x-1)`?

Answer 1

`-2/3x^2+19/9x-17/27-44/(81x-27)`

Explanation:

`color(white)("ddddddd.ddddddd")-2x^3+7x^2-4x-1`
`color(magenta)(-2/3x^2)(3x-1) ->ul(-2x^3+2/3x^2 larr" Subtract")`
`color(white)("ddddddddddddddddd")0+19/3x^2-4x-1`

`color(magenta)(+19/9x)(3x-1)->color(white)("ddddd.")ul(19/3x^2-19/9xlarr" Subtract")`
`color(white)("dddddddddddddddddddddd")0color(white)("dd")-17/9x-1`

`color(magenta)(-17/27)(3x-1) ->color(white)("dddddddddddd")ul( -17/9x+17/27larr" Subtract")`
`color(magenta)("Remainder"-> color(white)("ddddddddddddddddd")0color(white)("d")-44/27)`

`color(magenta)(-2/3x^2+19/9x-17/27 -[44/27color(black)(-:(3x-1))])`

`-2/3x^2+19/9x-17/27-44/(81x-27)`