# How do you use synthetic division to divide 4a^2 + 19a + 21 by a+1?

Oct 14, 2015

$4 {a}^{2} + 19 a + 21$ divided by $a + 1$

$a + 1 = a - \left(- 1\right)$

$\text{-1} | |$ $\text{4 " " " "19 " " " "21 }$
$+$ $\text{ " " " " "" "-4" " " " -15" }$
$\text{ " }$$- - - - - -$
$\text{ "" "4" "15" "|6" }$

The quotient is $4 a + 15$ and the remainder is $6$

We can check our answer by finding:

$\left(a + 1\right) \left(4 a + 15\right) + 6$

$= 4 {a}^{2} + 15 a + 4 a + 15 + 6$

$= 4 {a}^{2} + 19 a + 21$ which is the dividend.