Question

How do you divide #(-x^3+6x^2-2x+1) / (x-3) # using polynomial long division?

Answer 1

`(-x^3+6x^2-2x+1)/(x-3)=color(blue)(-x^3+3x+7" remainder: "22)`
(see below for solution using polynomial long division)

Explanation:

`color(white)("XXX)")ul(color(white)("x")-x^2color(white)("x")+3xcolor(white)("x.")+7color(white)("xxxxxxx"))`
`x-3)-x^3color(white)("x")+6x^2color(white)("x")-2xcolor(white)("x")+1`
`color(white)("XXxX)")ul(-x^3color(white)("x")+3x^2)`
`color(white)("XXXXXXXX..")3x^2color(white)("x")-2x`
`color(white)("XXXXXXXX..")ul(3x^2color(white)("x")-9x)`
`color(white)("XXXXXXXXXXXXX")7xcolor(white)("x")+1`
`color(white)("XXXXXXXXXXXXX")ul(7x-21)`
`color(white)("XXXXXXXXXXXXXXXX")22`