Answer
$(x-5)(5x-1)$
Work Step by Step
The given quadratic trinomial has $a=5, b=-26,$ and $c=5$.
Factor using the AC-method.
Note that $\text{AC}=5(5)=25$.
Look for factors of $25$ whose sum is equal to the value of $b$, which in this case is $-26$.
Note that:
$(-25)(-1) = 25$ and $-25+(-1)=-26$
Rewrite $-26x$ as $-25x -x$ to obtain:
\begin{align*}
5x^2-26x+5&=5x^2-25x-x+5\\
&=(5x^2-25x)+(-x+5)
\end{align*}
Factor out $5x$ in the first group and $-1$ in the second to obtain:
\begin{align*}
&=5x(x-5)+(-1)(x-5)
\end{align*}
Factor out $x-5$ to obtain:
\begin{align*}
&=(x-5)(5x-1)\\
\end{align*}
