Question

How do you divide `(x^4+2x^3+ 5 x^2+6x-32)/(x-4)`?

Answer 1

The remainder is `=456` and the quotient is `=x^3+6x^2+29x+122`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `4` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `2` `color(white)(aaaaaa)` `5` `color(white)(aaaaa)` `6` `color(white)(aaaaaaa)` `-32`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `4` `color(white)(aaaaaa)` `24` `color(white)(aaaa)` `116` `color(white)(aaaaaa)` `488`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaa)` `6` `color(white)(aaaaaa)` `29` `color(white)(aaaa)` `122` `color(white)(aaaaaa)` `color(red)(456)`

`(x^4+2x^3+5x^2+6x-32)/(x-4)=(x^3+6x^2+29x+122)+(456)/(x-4)`

The remainder is `=456` and the quotient is `=x^3+6x^2+29x+122`