Question

Factor x4–16 completely.
x2+x–x+
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Answer 1

x^4 − 16 is a difference of squares:
x^4 − 16 = (x^2 − 4)(x^2 + 4).

Then x^2 − 4 is also a difference of squares:
x^2 − 4 = (x − 2)(x + 2).

So over the reals:
x^4 − 16 = (x − 2)(x + 2)(x^2 + 4).

If you want the complete factorization over the complex numbers:
x^4 − 16 = (x − 2)(x + 2)(x − 2i)(x + 2i).

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