Call those roots respectively. Clearly none of the linear factors is in Z[x]. So if there is a factorisation in Z[x] it must consist of a quadratic factor and a cubic factor. The two complex linear factors must obviously belong in the same real factor, hence so must their product . But 2d is not an integer, so that quadratic expression is not in Z[x]. Notice however that a=-2d, which raises the possibility that the cubic factor might be in Z[x]. If so, then the quadratic factor would be the product of the remaining two linear factors. Use your calculator to find b+c and bc, to see whether they look like integers.