Question

How do you divide #(x^3+4x^2-3x-12) / (x^2-3) # using polynomial long division?

Answer 1

`x+4`

Explanation:

Using place keeper of no value. Example `0x^2`

`color(white)("ddddddddddd")x^3+4x^2-3x-12`
`color(magenta)(x)(x^2-3)-> color(white)(".")ul(x^3+0x^2-3xlarr" Subtract")`
`color(white)("ddddddddddd.")0color(white)("d")+4x^2+0x-12`
`color(magenta)(4)(x^2-3)->color(white)("dddd..")ul(4x^2+0x-12larr" Subtract"`
`color(white)("dddddddddddddddd")0color(white)("d")+0color(white)("d")+0`

`(x^3+4x^2-3x-12)/(x^2-3) = color(magenta)(x+4)`