What are the factors of x^4 − 1?
The factors of x^4 - 1 can be found using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
Applying this formula to x^4 - 1, we have:
x^4 - 1 = (x^2)^2 - 1^2
Using the difference of squares formula again, this can be further simplified as:
(x^2 + 1)(x^2 - 1)
The second factor, x^2 - 1, can again be factored using the difference of squares formula:
(x^2 + 1)(x + 1)(x - 1)
Therefore, the factors of x^4 - 1 are (x^2 + 1)(x + 1)(x - 1).