Question

How do you divide `(5x^3-6x^2+3x+11)div(x-2)` using synthetic division?

Answer 1

The remainder is `=33` and the quotient is `=5x^2+4x+11`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `2` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `5` `color(white)(aaaa)` `-6` `color(white)(aaaa)` `3` `color(white)(aaaa)` `11`
`color(white)(aaaaaaaaaaaa)`____________

`color(white)(aaaa)` #color(white)(aaaaaaa)|# `color(white)(aaaa)` #color(white)(aaaaa)10# `color(white)(aaaa)` `8` `color(white)(aaaa)` `22`
`color(white)(aaaaaaaaaaaa)`____________
`color(white)(aaaa)` #color(white)(aaaaaaa)|# `color(white)(aaaa)` `5` `color(white)(aaaa)` `4` `color(white)(aaaaa)` `11` `color(white)(aaaa)` `color(red)(33)`

The remainder is `=33` and the quotient is `=5x^2+4x+11`