Question

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

Answer 1

Although it may look different to what you were shown this really is the same process as traditional long division. It is just that this format works well for Socratic's web page system.

`x^2+4x+7+9/(x-1)`

Explanation:

`color(white)("dddddddddd.")x^3+3x^2+3x+2`
`color(magenta)(x^2)(x-1) -> ul(x^3-color(white)("d")x^2 larr" Subtract")`
`color(white)("ddddddddddd")0+4x^2+3x+2`
`color(magenta)(4x)(x-1)->color(white)("ddd.") ul(4x^2-4xlarr" Subtract")`
`color(white)("ddddddddddddddd")0color(white)("d")+7x+2`
`color(magenta)(7)(x-1) -> color(white)("ddddddddd.")ul(7x-7larr"Subtract" )`
`color(white)("dddddddddddddddddddd")0+color(magenta)(9 larr" Remainder")`

`color(magenta)(x^2+4x+7+9/(x-1))`