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

Oct 16, 2017

Remainder: $10$

#### Explanation:

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

$f \left(- 1\right) = {\left(- 1\right)}^{4} - 3 {\left(- 1\right)}^{2} + 12$
$= 10$

The remainder is $10$.

Oct 16, 2017

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
$x + 1 | \overline{{x}^{4} + 0 - 3 {x}^{2} + 0 + 12}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \underline{{x}^{4} + {x}^{3}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots} - {x}^{3} - 3 {x}^{2}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \underline{- {x}^{3} - {x}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} - 2 {x}^{2} + 0$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{- 2 {x}^{2} - 2 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 2 x + 12$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \underline{2 x + 2}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 10$

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