# How do you divide (a^3+5a^2+14a+16)div(a+2) using synthetic division?

Oct 22, 2016

The result is ${a}^{2} + 3 a + 8$

#### Explanation:

Let's do the division

${a}^{3} + 5 {a}^{2} + 14 a + 16$ color(white(aa))∣$a + 2$
${a}^{3} + 2 {a}^{2}$$\textcolor{w h i t e}{a a a a a a a a a}$∣${a}^{2} + 3 a + 8$
$0 + 3 {a}^{2} + 14 a$
$\textcolor{w h i t e}{a a a a}$$3 {a}^{2} + 6 a$
$\textcolor{w h i t e}{a a a a a a a a a a}$$8 a + 16$
$\textcolor{w h i t e}{a a a a a a a a a a}$$8 a + 16$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 + 0$

So the result of the division is ${a}^{2} + 3 a + 8$