For individual or collaborative investigation (Exercise 1)
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
Compare your answers in Exercises 2 and 3. Based on these results, what is the factorization of x4 + x2 + 1?
Exercise 2
For individual or collaborative investigation (Exercise 2)
The polynomial x6 – 1 can be considered either a difference of squares or a difference of cubes. Work Exercise 4, to connect the results obtained when two different methods of factoring are used.
Exercise 4
Factor x6 – 1 by first factoring as the difference of squares, and then factor further by using the patterns for the sum of cubes and the difference of cubes.
Exercise 3
For individual or collaborative investigation (Exercise 3)
The polynomial x6 – 1 can be considered either a difference of squares or a difference of cubes. Work Exercise 5, to connect the results obtained when two different methods of factoring are used.
Exercise 5
Factor x6 – 1 by first factoring as the difference of cubes, and then factor further by using the pattern for the difference of squares.
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