The complex conjugate root theorem states that if the coefficients of a polynomial are real, then the non-real roots appear in pairs of the type a ± ib thus

The roots of the polynomial are: 4 + 5i, 4 - 5i and 4 with multiplicity 2 and we can write the polynomial

f(x) = (x - (4 + 5i))(x - (4 - 5i))((x - 4)^2) = (x^2 - x(4 - 5i + 4 + 5i) + (16 + 25))(x^2 - 8x + 16) =

= (x^2 - 8x + 41)(x^2 - 8x + 16) = x^4 - 16x^3 + 121x^2 - 456x + 656

f(x) = x^4 - 16x^3 + 121x^2 - 456x + 656