Answer: The correct option is
(C) [tex](k+10f)(k-5f).[/tex]
Step-by-step explanation: We are given to factor the following quadratic expression :
[tex]E=k^2+5kf-50f^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To factor the given expression, we must find two integers with sum 5 and product -50.
The factorization of given expression (i) is as follows :
[tex]E\\\\=k^2+5kf-50f^2\\\\=k^2+10kf-5kf-50f^2\\\\=k(k+10f)-5f(k+10f)\\\\=(k+10f)(k-5f).[/tex]
Thus, the required factored form of the given expression is [tex](k+10f)(k-5f).[/tex]
Option (C) is CORRECT.
