# How do you find the quotient and remainder when (3x^3-2x^2+x+7) is divided by (x^2-2x+5)?

Nov 6, 2016

The remainder is $= - 6 x - 13$
The quotient is $= 3 x + 4$

#### Explanation:

Let's do the long division
$\textcolor{w h i t e}{a a a a}$$3 {x}^{3} - 2 {x}^{2} + x + 7$$\textcolor{w h i t e}{a a a}$∣${x}^{2} - 2 x + 5$
$\textcolor{w h i t e}{a a a a}$$3 {x}^{3} - 6 {x}^{2} + 15 x$$\textcolor{w h i t e}{a a a a a}$∣$3 x + 4$
$\textcolor{w h i t e}{a a a a a a}$$0 + 4 {x}^{2} - 14 x + 7$
$\textcolor{w h i t e}{a a a a a a a a}$$+ 4 {x}^{2} - 8 x + 20$
$\textcolor{w h i t e}{a a a a a a a a a a}$$+ 0 - 6 x - 13$

The remainder is $= - 6 x - 13$
The quotient is $= 3 x + 4$