Answer
a) $\frac{4 x^2-25 x-21}{x-7}=4x+3$
b) $ (x-7)\cdot (4x+3)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(4 x^2-25 x-21\right) \div(x-7).
\end{aligned}
\end{equation} Use synthetic division.
\begin{equation}
\begin{array}{r|rrr}
7&4 & -25 & -21\\
& & 28 & 21\\
\hline &4& 3 & 0
\end{array}
\end{equation} a) The solution is
\begin{equation}
\begin{aligned}
\frac{4 x^2-25 x-21}{x-7}=4x+3.
\end{aligned}
\end{equation}
b) The prime factor decomposition is $$ (x-7)\cdot (4x+3).$$
