Question

How do you use synthetic division to divide `x^4+4x^3+6x^2+4x+1` by `x+1`?

Answer 1

The remainder is `0` and the quotient is `=x^3+3x^2+3x+1`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-1` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `4` `color(white)(aaaaaa)` `6` `color(white)(aaaa)` `4` `color(white)(aaaaa)` `1`

`color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaa)` `-1` `color(white)(aaaa)` `-3` `color(white)(aaa)` `-3` `color(white)(aaa)` `-1`

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

`color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `3` `color(white)(aaaaaa)` `3` `color(white)(aaaa)` `1` `color(white)(aaaaa)` `color(red)(0)`

The remainder is `0` and the quotient is `=x^3+3x^2+3x+1`

`(x^4+4x^3+6x^2+4x+1)/(x+1)=x^3+3x^2+3x+1`