Respuesta :
Answer: The correct option is (C) [tex](p-6)(p+4).[/tex]
Step-by-step explanation: We are given to factor the following quadratic expression :
[tex]E=p^2-2p-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To factor the given expression, we need two integers with sum -2 and product -24. Those two integers are -6 and 4.
The factorization of expression (i) is as follows :
[tex]E\\\\=p^2-2p-24\\\\=p^2-6p+4p-24\\\\=p(p-6)+4(p-6)\\\\=(p-6)(p+4).[/tex]
Thus, the required factored form of the given expression is [tex](p-6)(p+4).[/tex]
Option (C) is CORRECT.
