1. You should have

.

Convert to polar form:

.

Consider the case

.

Let

so that

.

We get

.

The rest is very similar to the process of finding the roots of unity. We want to solve

for some integer

. Re-arrange to get

We're looking for cube roots, so we should expect to find three distinct answers. Set

in the above to get your solutions.

Now do the same for the other case

.

2. The (relatively) obvious method is to find all the roots of

and in this way factorise the polynomial into linear factors, and then multiply the linear factors back together in a way that creates real quadratic factors.

Here's a cleaner way to do this.

First make the substitution

. The polynomial then becomes

We just need to factorise

.

Now, I propose that you can write this polynomial in the form

.

Why this choice? Notice the coefficient of

is

, so we would expect the coefficients of

in each factor to also be

. The constant term is also

, so we should expect the constant terms in each factor to be

as well.

You can expand the RHS and equate coefficients on each side to find

. Remember to substitute back for

when you're done.

(As an exercise, you can try the same thing with the polynomial you obtained,

.)

3. Just write

. It's already in the form

, where

.