We will use the following Theorem:

If P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P

If one zero is -5+3i then also -5-3i is a zero. 

(x - (-5+3i))(x - (-5 - 3i))*(x - 4)^2 = x^4 + 2x^3 - 30x^2 - 112x + 544

click here to see the step by step solution

F (x) = x^4 + 2x^3 - 30x^2 - 112x + 544