Answer:
f(x) = x^3 + 2 x^2 + 16 x + 32
or also
f(x) = k (x^3 + 2 x^2 + 16 x + 32)
Step-by-step explanation:
Given that -2, 4i and - 4i are roots, then the binomial factors to be included are:
(x - - 2) (x - 4i) (x --4i) = (x + 2) (x - 4i) (x + 4i) =
(x + 2 ) (x^2 - x 4i + x 4i - 16 i^2) = (x + 2) (x^2 + 16) =
x^3 + 16 x + 2 x^2 + 32
which in standard form reads:
x^3 + 2 x^2 + 16 x + 32
Also have in mind that the polynomial could also include a constant multiplicative factor "k".
