The graph's zeros at x = 1, x = 4, and a double zero at x = -3/2 indicate the function form: p(x) = a(x - 1)(x - 4)(2x + 3)^2, where a is positive.
The correct answer is: p(x) = (x - 1)(х - 4)(2x + 3)^2
This can be inferred from the graph of the function. The function has zeros at x = 1 and x = 4, and it has a double zero at x = -3/2. This means that the function is of the form:
p(x) = a(x - 1)(x - 4)(2x + 3)^2
where a is a constant. The graph also shows that the function is positive between its zeros, and negative outside of its zeros. This means that the constant a must be positive.
Therefore, the equation of the function is p(x) = (x - 1)(х - 4)(2x + 3)^2.