Question

How do you divide `(3x^4-2x^3+5x^2-4x-2)div(x+1)` using synthetic division?

Answer 1

The remainder is `=12` and the quotient is `=3x^3-5x^2+10x-14`

Explanation:

Let's perform the synthetic division

Let `f(x)=3x^4-2x^3+5x^2-4x-2`

Let's perform the synthetic division

`color(white)(aaaa)` `-1` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `3` `color(white)(aaaaaa)` `-2` `color(white)(aaaaaa)` `5` `color(white)(aaaaa)` `-4` `color(white)(aaaaa)` `-2`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaa)` `-3` `color(white)(aaaaaaa)` `5` `color(white)(aaaaa)` `-10` `color(white)(aaaa)` `14`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `3` `color(white)(aaaaaa)` `-5` `color(white)(aaaaaaa)` `10` `color(white)(aaaa)` `-14` `color(white)(aaaaa)` `color(red)(12)`

`f(x)=(3x^3-5x^2+10x-14)+12/(x+1)`

The remainder is `=-2`