Factor p 2 - 2p - 24. (p - 3)(p + 8) (p + 6)(p - 4) (p - 6)(p + 4)
Answer: The correct option is (C) \((p-6)(p+4).\)
Step-by-step explanation: We are given to factor the following quadratic expression :
\(E=p^2-2p-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
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 :
\(E\\\\=p^2-2p-24\\\\=p^2-6p+4p-24\\\\=p(p-6)+4(p-6)\\\\=(p-6)(p+4).\)
Thus, the required factored form of the given expression is \((p-6)(p+4).\)
Option (C) is CORRECT.