How do you factor out x to the fourth power minus 1?

Answer 1

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To factor that, you can use a principle called the difference of squares: any polynomial in the format a2 - b2 can be factored out to (a + b)(a - b). In this case, x4 is equal to x22, and 1 = 12, so we can say:

x4 - 1

= (x2 + 1)(x2 - 1)

You may note that the second factor is itself another difference of squares, so we can actually repeat that process:

= (x2 + 1)(x + 1)(x - 1)