Answer
$(x-3)(7x-16)$
Work Step by Step
First, since the polynomial $x^2 - 6x + 9$ is a perfect square, we can factor it using the formula $a^2-2ab+b^2=(a-b)^2$, where $a=x$ and $b=3$:
$$
7(x^2 - 6x + 9) + 5(x - 3)=7(x-3)^2 +5(x -3)
.$$
Then, factoring $x-3$ out gives
$$
7(x-3)^2 +5(x -3)= (x-3)[7(x-3)+5]
.$$
Finally, we distribute $7$ then combine like terms to obtain:
\begin{align*}
(x-3)[7(x-3)+5]&= (x-3)[7x-21+5] \\
&=(x-3)(7x-16).
\end{align*}
