The polynomial x6 – 1 can be considered either a difference of squares or a difference of...

The polynomial x6 – 1 can be considered either a difference of squares or a difference of cubes. Work Exercise 1, to connect the results obtained when two different methods of factoring are used.

Exercise 1

Factor x8 + x4 + 1 using the technique outlined in Exercise 2.

Exercise 2

The polynomial x6 – 1 can be considered either a difference of squares or a difference of cubes. Work Exercise 2, to connect the results obtained when two different methods of factoring are used.

The polynomial x4 + x2 + 1 cannot be factored using the methods described in this section. However, there is a technique that allows us to factor it, as shown here. Supply the reason that each step is valid.