Question

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

Answer 1

`color(magenta)((x^2+5x+1) / (x+3) = x+2` and remainder of`color(magenta)(-5/(x+3)`

Explanation:

`color(white)(aaaa)` `-3` `color(white)(aaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `5` `color(white)(aaaaa)` `1` `color(white)(aaaaaa)` `color(white)(aaaaaa)`

`color(white)(aaaaaa)` `color(white)(aaaaa)` `|` `color(white)(aaa)` `color(white)(aaaa)` `-3` `color(white)(aaaa)` `-6` `color(white)(aaaaa)` `color(white)(aaaaaa)`

`color(white)(aaaaaaaaaa)`---------------------------------------------

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `1` `color(white)(aaaaa)` `2` `color(white)(aaaaa)` `color(white)(a)` `-5` `color(white)(aaaaaa)`

The remainder is `color(magenta)(=-5/(x+3)`

The quotient is `color(magenta)(=x+2`