Find possible values of the constant p if the expression Px + 12x + 4p + px2 is a perfect square.

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1. Find possible values of the constant p if the expression $Px + 12x + 4p + px^2$ is a perfect square.

Assuming the capitalized 'P' is a typo and should be 'p', the expression is $px^2 + (p+12)x + 4p$.
For a quadratic expression $ax^2 + bx + c$ to be a perfect square, its discriminant must be zero ($b^2 - 4ac = 0$).
Here, $a = p$, $b = p+12$, and $c = 4p$.

Step 1: Set the discriminant to zero.

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