Answer:
the value of p is 7
Explanation:
Given function;
f(x) = 2x³ - 7px + (p - 12)
factor of the given function = x - 5
Apply remainder theorem to solve for p
f(x - 5) = 0
x - 5 = 0
x = 5
f(5) = 2(5)³ - 7p(5) + (p - 12) = 0
2(125) - 35p + p - 12 = 0
250 - 34p - 12 = 0
238 - 34p = 0
34p = 238
p = 238/34
p = 7
Therefore, the value of p is 7