Let f(x)=x^5-120x^4+1152x^3+341x^2-1185x-21945

The roots of this, as presented by the computer, happen to be

3.041032416, 109.44694126, 10.55305874, -1.520516208 +/- 1.983912452 i

Using only the roots, is f(x) reducible in Z[x]?

I'm a little confused how to go about this...do you just multiply together possible combinations and see if integers result, or is there a more efficient way?