# How do you divide (x^3 + x^2 +4x -6) / (x^2 -3x +2)  using polynomial long division?

##### 1 Answer
Dec 23, 2016

The quotient is $= \left(x + 4\right)$ and the remainder $= 14 \left(x - 1\right)$

#### Explanation:

Let's do the long division

$\textcolor{w h i t e}{a a a a}$${x}^{3} + {x}^{2} + 4 x - 6$$\textcolor{w h i t e}{a a a a}$∣${x}^{2} - 3 x + 2$

$\textcolor{w h i t e}{a a a a}$${x}^{3} - 3 {x}^{2} + 2 x$$\textcolor{w h i t e}{a a a a a a}$∣$x + 4$

$\textcolor{w h i t e}{a a a a a}$$0 + 4 {x}^{2} + 2 x - 6$

$\textcolor{w h i t e}{a a a a a a a}$$+ 4 {x}^{2} - 12 x + 8$

$\textcolor{w h i t e}{a a a a a a a a a}$$0 + 14 x - 14$

Therefore,

$\frac{{x}^{3} + {x}^{2} + 4 x - 6}{{x}^{2} - 3 x + 2} = x + 4 + \frac{14 \left(x - 1\right)}{{x}^{2} - 3 x + 2}$

$= x + 4 + \frac{14 \left(x - 1\right)}{\left(x - 2\right) \left(x - 1\right)}$

The quotient is $= \left(x + 4\right)$ and the remainder $= 14 \left(x - 1\right)$