Question

How do you divide `(x^4-3x^2+12)div(x+1)`?

Answer 1

Remainder: `10`

Explanation:

Using the Remainder Theorem, substitute `x=-1` into the equation.

`f(-1)=(-1)^4-3(-1)^2+12`
`=10`

The remainder is `10`.

Answer 2

`color(magenta)(x^3-x^2-2x+2` and remainder of `color(magenta)(10/(x+1)`

Explanation:

`color(white)(.......)color(white)(..)color(magenta)(x^3-x^2-2x+2`
`x+1|overline(x^4+0-3x^2+0+12)`
`color(white)(............)ul(x^4+x^3)`
`color(white)(...............)-x^3-3x^2`
`color(white)(................)ul(-x^3-x^2)`
`color(white)(.......................)-2x^2+0`
`color(white)(.........................)ul(-2x^2-2x)`
`color(white)(......................................)2x+12`
`color(white)(.......................................)ul(2x+2)`
`color(white)(..............................................)10`

`color(magenta)((x^4+3x^2+12) / (x+1) = x^3-x^2-2x+2` and remainder of `color(magenta)(10/(x+1)`