Question

How do you divide `(3x^4+9x^3-2x^2+2x-7)/(x-2)`?

Answer 1

The remainder is `=109` and the quotient is `=3x^3+15x^2+28x+58`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `2` `color(white)(aaaa)` `|` `color(white)(aaaa)` `3` `color(white)(aaaa)` `9` `color(white)(aaaaa)` `-2` `color(white)(aaaa)` `2` `color(white)(aaaaa)` `-7`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaa)` `6` `color(white)(aaaaaa)` `30` `color(white)(aaa)` `56` `color(white)(aaaaa)` `116`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `3` `color(white)(aaa)` `15` `color(white)(aaaaa)` `28` `color(white)(aaa)` `58` `color(white)(aaaaa)` `color(red)(109)`

The remainder is `=109` and the quotient is `=3x^3+15x^2+28x+58`

Therefore,

`(3x^4+9x^3-2x^2+2x-7)/(x-2)=3x^3+15x^2+28x+58+(109)/(x-2)`