Question

What is `(6x^3-18x^2-12x)/(-6x)`?

Answer 1

`-x^2+3x+2`

Explanation:

`"each term on the numerator is divided by "-6x`

`=(6x^3)/(-6x)-(18x^2)/(-6x)-(12x)/(-6x)`

`=(cancel(6)x^((3-1)))/-cancel(6)-(cancel(18)^3x^((2-1)))/(-cancel(6)^1)-cancel(12x)^2/(-cancel(6x)^1)`

`=-x^2+3x+2`

Answer 2

`color(crimson)(-x^2+3x+2`

Explanation:

`color(crimson)((6x^3-18x^2-12x)/(-6x)`

`color(white)(..)color(white)(....)-x^2+3x+2`
`-6x|overline(6x^3-18x^2-12x)`
`color(white)(..........)6x^3`
`color(white)(................)overline(-18x^3)`
`color(white)(................)ul(-18x^3)`
`color(white)(..........................)-12x`
`color(white)(............................)ul(-12x)`

`color(crimson)((6x^3-18x^2-12x) / (-6x) = -x^2+3x+2`