I presume you can to factor this, based on your other post on irreducible polynomials?Originally Posted by harold
I am not going to do every single step, you are a big boy you can handle it yourself.Originally Posted by harold
As you understand (I hope),
In order to use de Moiver's theorem you write,
Now you use de Moiver's theorem (actually it is not cuz his theorem if for integral exponents not rational).
Thus,
And each solution is for
That is the factorization in , good. Now find its factorization in . The trick is to look for the conjugates. Remember that, , where is no longer complex and is no longer complex.Originally Posted by harold
The first pair of conjugates are,
The polynomial they produce is,
The other pairs of conjugates are,
The polynomial they produce is,
So the factorization of,
in is,