Question

How do you divide `(3x^3+4x^2+2x+5)/(x-4)` ?

Answer 1

The remainder is `269` and the quotient is `=3x^2+16x+66`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `4` `|` `color(white)(aaaa)` `3` `color(white)(aaaa)` `4` `color(white)(aaaaaa)` `2` `color(white)(aaaaaaa)` `5`

`color(white)(aaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaa)` `12` `color(white)(aaaaa)` `64` `color(white)(aaaaa)` `264`

`color(white)(aaaaaaaaa)`##_________

`color(white)(aaaaa)` `|` `color(white)(aaaa)` `3` `color(white)(aaaa)` `16` `color(white)(aaaaa)` `66` `color(white)(aaaaaa)` `color(red)(269)`

The remainder is `269` and the quotient is `=3x^2+16x+66`

`(3x^3+4x^2+2x+5)/(x-4)=(3x^2+16x+66)+(269)/(x-4)`