Find an nth-degree polynomial function with real coefficients satisfying the given conditions. if you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3 4 and 4i are zeroes, f(2)= -40

Polynomials with real coefficients have complex roots in conjugate pairs. If 4i is a root, then so is -4i. So, now we have the three roots we need for a 3rd degree polynomial.
.. f(x) = a(x -4)(x -4i)(x +4i)
.. f(x) = a(x -4)(x^2 +16)
.. f(2) = a(-2)(4 +16) = -40a
.. -40 = -40a
.. 1 = a

The polynomial is f(x) = x^3 -4x^2 +16x -64