Question

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

Answer 1

`-x^2-3x+1+(16x)/(x^2+3)`

Explanation:

Using place keepers of zero value. Example: `0x^3`

`color(white)("dddddddddddddd")+x^4-3x^3-2x^2+7x+3`
`color(magenta)(-x^2)(x^2+3)->color(white)("d") ul(-x^4+0x^3-3x^2larr" Subtract")`
`color(white)("dddddddddddddddd")0 -3x^3+x^2+7x+3`
`color(magenta)(-3x)(x^2+3) -> color(white)("dddd")ul(-3x^3+0x^2-9xlarr" Subtract")`
`color(white)("ddddddddddddddddddddd")0+x^2+16x+3`
`color(magenta)(+1)(x^2+3)->color(white)("dddddddddddd")ul(x^2+color(white)("..")0x+3larr" Subtract")`
`color(magenta)("Remainder "->color(white)("dddddddddddd.")0+16x+0)`

`color(white)()`

`-x^2-3x+1+(16x)/(x^2+3)`