Answer: the correct option is
(C) [tex](p-10)(p+2).[/tex]
Step-by-step explanation: We are given to factor the following quadratic expression :
[tex]E=p^2-8p-20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To factor the given expression, we need to find two integers with sum -8 and product -20.
The factorization of expression (i) is as follows :
[tex]E\\\\=p^2-8p-20\\\\=p^2-10p+2p-20\\\\=p(p-10)+2(p-10)\\\\=(p-10)(p+2).[/tex]
Thus, the required factored form is [tex](p-10)(p+2).[/tex]
Option (C) is CORRECT.
