Question

How do you divide `9x ^ { 2} - 6x + 2` by `(-1+3x)`?

Answer 1

You must use polynomial division rules, and keep in mind that if using synthetic division, the divisor must be in the form x-a.

Explanation:

Change the divisor to the form of x-a:

`-1 +3x=0`
`3x=1`
`x=1/3`

Now, you can use long division or synthetic division and divide `9x2−6x+2` by `1/3`:

Answer 2

`color(magenta)((9x^2-6x+2) / (-1+3x) = 3x-1` and remainder of `color(magenta)1`

Explanation:

`color(white)(..........)color(white)(...)3x-1`
`3x-1|overline(9x^2-6x+2)`
`color(white)(............)ul(9x^2-3x)`
`color(white)(......................)-3x+2`
`color(white)(.......................)ul(-3x+1)`
`color(white)(...................................)1`

`color(magenta)((9x^2-6x+2) / (-1+3x) = 3x-1` and remainder of `color(magenta)1`