Using the distributive properly of the expressions, we can simplify the given complicated expression into,
(2)(x + 4)(x - 2p)
(2x + 8)(x - 2p)
2x² + 4px + 8x + 16p
Grouping of like terms,
2x² + (4p + 8)x + 16p
Then, we derive the equation and equate to zero to get the minimum,
4x + (4p + 8) = 0
It is given that the minimum value for x is equal to -18. Substitute -18 to the x from the above equation,
4(-18) + (4p + 8) = 0
Simplifying,
4p - 64 = 0,
p = 16
The value of p is then equal to 16
ANSWER: p = 16
