Question

How do you long divide `(4x^3-6x^2+5)div(x^2-4)`?

Answer 1

`4x-6` with remainder: `(16x-19)`

Explanation:

Assuming you are familiar with the process for "normal" long division:

`color(white)("XXXX")ul(color(white)("xx")4xcolor(white)("x")-6color(white)("xxxxxxxxxxxx")`
`x^2-4)color(white)("x")4x^3color(white)("x")-6xcolor(white)("x")color(grey)(+0x)color(white)("x")+5`
`color(white)("XXXXX")ul(4x^3color(white)("xxxxx")-16xcolor(white)("xxxx"))`
`color(white)("XXXXXXXX")-6x+16xcolor(white)("x")+5`
`color(white)("XXXXXXXX")ul(-6xcolor(white)("xxxxxx")+24`
`color(white)("XXXXXXXXXXXXX")16x-19`