Answer
a) $\frac{4 x^2+5 x-21}{x+3}=4x-7$
b) $ (x+3)\cdot (4x-7)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(4 x^2+5 x-21\right) \div(x+3).
\end{aligned}
\end{equation} Use synthetic division.
\begin{equation}
\begin{array}{r|rrr}
-3&4 & 5 & 21\\
& & -12 & -21\\
\hline &4& -7 & 0
\end{array}
\end{equation} a) The solution is \begin{equation}
\begin{aligned}
\frac{4 x^2+5 x-21}{x+3}=4x-7.
\end{aligned}
\end{equation} b) The prime factor decomposition is $$ (x+3)\cdot (4x-7).$$
