B
1) As we can see all coefficients are divisible by 5. That leads us to opt to factor out the common factor technique.
[tex]\begin{gathered} 5x^2-5x-100 \\ \\ 5\left(x^2-x-20\right) \\ \\ \end{gathered}[/tex]
2) Now, let's focus on factoring the trinomial inside the parentheses. Note that we need to find two numbers whose sum is -1 and simultaneously their product is -20.
By guess and check, we know these numbers are -5 and 4.
[tex]\begin{gathered} -5+4=-1 \\ -5\times4=-20 \end{gathered}[/tex]
[tex]\begin{gathered} 5\lbrack\lparen x-5)(x+4)\rbrack \\ \\ 5(x-5)(x+4) \end{gathered}[/tex]
Thus, the answer is B
