Question

How do you find the quotient of `(9n^3-13n+8)div(3n-1)` using long division?

Answer 1

The quotient is `=3n^2+n-4`

Explanation:

Let's perform the long division

`color(white)(aaaa)` `9n^3` `color(white)(aaaaaa)` `-13n+8` `|` `3n-1`

`color(white)(aaaa)` `9n^3-3n^2` `color(white)(aaaaaaaaa)` ###|#`3n^2+n-4`

`color(white)(aaaaaa)` `0+3n^2-13n`

`color(white)(aaaaaaaa)` `+3n^2-n`

`color(white)(aaaaaaaaa)` `+0-12n+8`

`color(white)(aaaaaaaaaaaaa)` `-12n+4`

`color(white)(aaaaaaaaaaaaaaa)` `-0+4`

So,

`(9n^3-13n+8)/(3n-1)=(3n^2+n-4)+4/(3n-1)`