Question

How do you use the Remainder Theorem to find the remainder when `f(x)=-x^3+5x-9` is divided by `x-2`?

Answer 1

The answer is `f(2)=-7`

Explanation:

Let's run the long division

`-x^3` `color(white)(aaaaaa)` `5x` `color(white)(aa)` `-9` `∣` `x-2`
`-x^3+2x^2` `color(white)(aaaaa)` `color(white)(aa)` `∣` `-x^2-2x+1`
`color(white)(aa)` `0-2x^2+5x`
`color(white)(aaaa)` `-2x^2+4x`
`color(white)(aaaaaaaa)` `0+x-9`
`color(white)(aaaaaaaaaaa)` `x-2`
`color(white)(aaaaaaaaaaa)` `0-7`

So the remainder is -7, then `f(2)=-7`