Answer
$f(x)=x^4+2x^3-9x^2-22x-12$
Work Step by Step
Using the Factor Theorem, if $x=a$ is a factor, then $(x-a)$ is a factor of $f(x)$.
Hence here $f(x)=(x-(-3))(x-(-1))(x-(1-\sqrt 5))(x-(1+\sqrt 5))\\=(x+1)(x+3)(x-2i)(x-1+\sqrt 5)(x-1-\sqrt 5)\\=(x+1)(x+3)(x^2-2x-4)\\=(x^2+4x+3)(x^2-2x-4)\\=x^4+2x^3-9x^2-22x-12$
