Question

How do you divide `(6x^3-12x+10) div (3x-3)`?

Answer 1

`2x^2+2x-2+4/(x-3)`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(2x^2)(3x-3)color(magenta)(+6x^2)-12x+10`

`=color(red)(2x^2)(3x-3)color(red)(+2x)(3x-3)color(magenta)(+6x)-12x+10`

`=color(red)(2x^2)(3x-3)color(red)(+2x)(3x-3)color(red)(-2)(3x-3)color(magenta)(-6)+10`

`=color(red)(2x^2)(3x-3)color(red)(+2x)(3x-3)color(red)(-2)(3x-3)+4`

`rArr(6x^3-12x+10)/(3x-3)`

`=(cancel((3x-3))(color(red)(2x^2+2x-2)))/cancel((3x-3))+4/(3x-3)`

`=2x^2+2x-2+4/(3x-3)`

Answer 2

`color(green)((2x^2+2x-2)+4/(3x-3)`

Explanation:

`(6x^3-12x+10)-:(3x-3)`

`color(white)(.............)ul(color(green)(2x^2+2x-2)`
`color(white)(a)3x-3` `|` `6x^3+0-12x+10`
`color(white)(...............)ul(6x^3-6x^2)`
`color(white)(........................)6x^2-12x`
`color(white)(........................)ul(6x^2-6x)`
`color(white)(..............................)-6x+10`
`color(white)(...............................)ul(-6x+6)`
`color(white)(.......................................)color(green)(+4`

`color(white)(.............)color(green)((2x^2+2x-2)+4/(3x-3)`