Answer
$3x^2+5x+4$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(3 x^3+14 x^2+19 x+12\right) \div(x+3)
\end{aligned}
\end{equation} Use synthetic division.
\begin{equation}
\begin{array}{r|rrrr}
-3&3 & 14 & 19& 12 \\
& & -9 & -15& -12 \\
\hline & 3 & 5 & 4& 0
\end{array}
\end{equation} The solution is \begin{equation}
\begin{aligned}
\frac{3 x^3+14 x^2+19 x+12}{x+3}= 3x^2+5x+4
\end{aligned}
\end{equation}
