# How do you divide (6b^3+28b^2+25b-21)div(b+3) using synthetic division?

Feb 21, 2017

The quotient is $= 6 {b}^{2} + 10 b - 5$ and the remainder is $= - 6$

#### Explanation:

We perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 3$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$6$$\textcolor{w h i t e}{a a a a}$$28$$\textcolor{w h i t e}{a a a a a}$$25$$\textcolor{w h i t e}{a a a}$$- 21$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a a}$$\textcolor{w h i t e}{a a}$$- 18$$\textcolor{w h i t e}{a a a a}$$- 30$$\textcolor{w h i t e}{a a a a}$$15$

$\textcolor{w h i t e}{a a a a a a a a a a}$------------------------------------------------------------

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$$6$$\textcolor{w h i t e}{a a a a}$$10$$\textcolor{w h i t e}{a a a a}$$- 5$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{- 6}$

The remainder is $= - 6$

The quotient is $= 6 {b}^{2} + 10 b - 5$