Question

How do you find f(-3) given `f(x)=x^3-2x^2+4x+6` using synthetic division?

Answer 1

The remainder is `color(red)(-51)` and the quotient is `=x^2-5x+19`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-3` `color(white)(aaaaaa)` `|` `color(white)(aa)` `1` `color(white)(aaaa)` `-2` `color(white)(aaaaaa)` `4` `color(white)(aaaaaaa)` `6`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaa)` `-3` `color(white)(aaAaa)` `15` `color(white)(aaaaa)` `-57`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaaaa)` `-5` `color(white)(aaaaaa)` `19` `color(white)(aaaa)` `color(red)(-51)`

The remainder is `color(red)(-51)` and the quotient is `=x^2-5x+19`

Therefore,

`(x^3-2x^2+4x+6)/(x+3)=x^2-5x+19-51/(x+3)`