Question

How do you evaluate `f(x)=-x^4+8x^3+13x-4` at x=-2 using direct substitution and synthetic division?

Answer 1

The answer is `=-110`

Explanation:

Direct substitution

`f(-2)=-16-64-26-4=-110`

The remainder is `=-110`

We perform a synthetic division

`color(white)(aaaa)` `-2` `color(white)(aaaa)` `|` `color(white)(aaaa)` `-1` `color(white)(aaaa)` `8` `color(white)(aaaaa)` `0` `color(white)(aaaaaa)` `13` `color(white)(aaaa)` `-4`

`color(white)(aaaaaa)` `color(white)(aaaaa)` `|` `color(white)(aaa)` `color(white)(aaaaaaa)` `2` `color(white)(aaaaa)` `-20` `color(white)(aaaa)` `40` `color(white)(aaaaa)` `-106`

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

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `-1` `color(white)(aaa)` `10` `color(white)(aaaaa)` `-20` `color(white)(aaaaa)` `53` `color(white)(aaaaa)` `color(red)(-110)`

The remainder is `=-110`

The quotient is `=-x^3+10x^2-20x+53`