The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 3 and roots of multiplicity 1 at x = 0 and x = - 3. It goes through the point (5, 96). Find a formula for P(x).
P(x) =

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.