Question

How do you divide `(3x^3-6x^2+13x-4)/(x-3)`?

Answer 1

`3x^2+3x+22+62/(x-3)`

Explanation:

color(white)(.)
`" "3x^3-6x^2+13x-4`
`" "color(magenta)(3x^2)(x-3) ->" "ul(3x^3-9x^2)" "larr" Subtract"`
`" "0color(white)(.)+3x^2+13x-4`
`" "color(magenta)(3x)(x-3)->" "ul(3x^2-9x) larr" Subtract"`
`" "0+22x-4`
`" "color(magenta)(22)(x-3) ->" "ul(22x-66) larr" Subtract"`
`" "0color(magenta)(+62 larr" Remainder")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`3x^2+3x+22+62/(x-3)`