Question

How do you divide `(n^3+n^2-11n+18)div(n-1)` using synthetic division?

Answer 1

`color(blue)(" Quotient " n^2 + 2n -9, "Remainder " (-1/(n-1))`

Explanation:

`(n^3 + n^2 - 11n + 8) / (n - 1), "using synthetic division "`

`color(white)(aaa aaa aaa )`
`color(white)(aaa ) 1color(white)(aaa )|color(white)(aaa )1 color(white)(aaa )1 color(white)(a )-11color(white)(aaa )8`
`color(white)(aaa aaaa )|color(white)(aa )darrcolor(white)(aaa )1 color(white)(aaaa )2 color(white)(a )-9`
`color(white)(aaa aaa a )| --------`
`color(white)(aaa aaa aaa aaa)1 color(white)(aaa )2color(white)(aa ) -9 color(white)(a ) -1`

`color(blue)(" Quotient " n^2 + 2n -9, "Remainder " (-1/(n-1))`