Question

How do you use synthetic division to divide `(5x^3+6x+8)div(x+2)`?

Answer 1

The quotient is `=5x^2-10x+26` and the remainder is `=-44`

Explanation:

Let `f(x)=5x^3+6x+8`

Let's perform the synthetic division

`color(white)(aaaa)` `-2` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `5` `color(white)(aaaa)` `0` `color(white)(aaaAAAa)` `6` `color(white)(aaAaa)` `8`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` ###color(white)(aaaaaaa)#`|` `color(white)(aaaa)` ###color(white)(aaaa)#`-10` `color(white)(aaaaa)` `20` `color(white)(aaa)` `-52`
`color(white)(aaaaaaaaaaaa)`________
`color(white)(aaaa)` ###color(white)(aaaaaaa)#`|` `color(white)(aaaa)` `5` `color(white)(aaa)` `-10` `color(white)(aaaaa)` `26` `color(white)(aaa)` `color(red)(-44)`

`f(x)=(x+2)(5x^2-10x+26)-44`