Question

How do you divide `(x^3+6x^2-30x+102)div(x+10)` using synthetic division?

Answer 1

The result `(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)`

Explanation:

Let's do the division
`x^3+6x^2-30x+102` `color(white)(aaaaa)` `∣x+10`
`x^3+10x^2` `color(white)(aaaaaaaaaaaaaaa)` `∣x^2-4x+10`
`0- 4x^2-30x`
`color(white)(aa)` `-4x^2-40x`
`color(white)(aaaaa)` `0+10x+102`
`color(white)(aaaaaaaaa)` `10x+100`
`color(white)(aaaaaaaaaaa)` `0+2`

The remainder `=2`

so the result is `(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)`