Question

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

I changed `(-4^3) rarr (-4x^3)`. Sorry if this is not what was intended, but it seemed more likely.

Answer 1

`-4x^2-13x-36-112/(x-3)`

Explanation:

`" "-4x^3-x^2+3x-4`
`color(magenta)(-4x^2)(x-3) ->ul( -4x^3+12x^2) larr" Subtract"`
`" "color(white)(..)0-13x^2+3x-4`
`color(magenta)(-13x)(x-3)->" "ul(color(white)(..)-13x^2+39x)" "larr" Subtract"`
`" "0color(white)(..)-36x-4`
`color(magenta)(-36)(x-3)->" "color(white)(..)ul(-36x+108)" "larr" Subtract"`
`" "0color(white)(..)color(magenta)(-112 larr" Remainder")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(-4x^2-13x-36-112/(x-3))`