9514 1404 393
Answer:
f(x) = x^4 -x^3 +7x^2 -9x -18
Step-by-step explanation:
The imaginary root has a corresponding conjugate that is also a root. Each root has a corresponding factor: (x -p) for root p.
f(x) = (x -3i)(x +3i)(x -(-1))(x -2)
f(x) = (x^2 +9)(x^2 -x -2) . . . . combine pairs of factors
f(x) = x^4 -x^3 +7x^2 -9x -18 . . . . finish multiplying it out
__
We have made use of the products of binomials:
(x +a)(x +b) = x^2 +(a+b)x +ab
(x +a)(x -a) = x^2 -a^2
