The point of this exercise is to find the factorization of the polynomial on the left:
[tex]x^2{\textcolor{red}{+}}8x\textcolor{green}{-}65[/tex]
Its factorization has the form:
[tex](x{{\textcolor{red}{+}}a_1)}(x{\textcolor{green}{-}a_2}_{})[/tex]
where the first sign (red +) coincides with the first + above, and the second sign (green -) coincides with the product between the signs above (red + by the green - ). Now, we must find the missing (two) numbers a_1 and a_2. These numbers must satisfy:
[tex]\begin{cases}a_1-a_2=8 \\ a_1\cdot a_2=-65\end{cases}[/tex]
Solving this system "by eye", we get
[tex]a_1=13,a_2=5[/tex]
Then, the factorization is
[tex](x+13)(x-5)[/tex]
The answer would be C if there were a 13 instead of 12.
