Question

How do you divide `(a^3+5a^2+14a+16)div(a+2)` using synthetic division?

Answer 1

The result is `a^2+3a+8`

Explanation:

Let's do the division

`a^3+5a^2+14a+16` `color(white(aa))` `∣` `a+2`
`a^3+2a^2` `color(white)(aaaaaaaaa)` `∣` `a^2+3a+8`
`0+ 3a^2+14a`
`color(white)(aaaa)` `3a^2+6a`
`color(white)(aaaaaaaaaa)` `8a+16`
`color(white)(aaaaaaaaaa)` `8a+16`
`color(white)(aaaaaaaaaaa)` `0+0`

So the result of the division is `a^2+3a+8`