Question

Factor x4–16 completely.
x2+
x–
x+

Answer 1

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

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