Two important concepts to recall here: 1) The complex zeros for polynomials with real coefficients come in conjugate pairs. Thus, 4 + 2i is a zero means that its conjugate, 4 - 2i, is a zero also. 2) We use a constant, usually "a", to represent the lead coefficient for a polynomial in factored form whose zeros we know. Then, given a point on the graph, we can solve for the specific polynomial.
f(x) = a(x + 3)(x - (4 - 2i))(x - (4 + 2i))
= a(x + 3)(x2 - 8x + 20)
= a(x3 - 5x2 - 4x + 60)
f(1) = a(52) = 52 so a = 1
f(x) = x3 - 5x2 - 4x + 60
