Find possible values of the constant p if the expression Px² - 12x + 4p is a perfect square.

Here are the solutions to the questions:

1. Find possible values of the constant $p$ if the expression $Px^2 - 12x + 4p$ is a perfect square.
For a quadratic expression $Ax^2 + Bx + C$ to be a perfect square, its discriminant must be zero, i.e., $B^2 - 4AC = 0$.
In this expression, $A = P$, $B = -12$, and $C = 4p$.

Step 1: Set the discriminant to zero.

$$(-12)^2 - 4(P)(4p) = 0$$

Step 2: Simplify the equation.

$$$$