Linear factors are , the conjugate pair and (since the conjugate root theorem is valid), and . Therefore .....

I was tempted to add as a factor so that is a quadratic factor and you have a nice simple polynomial, but then the resulting polynomial is not of least degree.

and I'm sure you know how to factorise a difference of two cubes.

Both can be done using a calculator. What's actually required here? A technology free simplification (in which case nothing needs to be done with the second) .....?