### Instruction: Factor $w^4-16$ as far as possible, where the factors are monic polynomials with real coefficients.### Response: I know that this is a difference of squares, so I can apply the formula $a^2-b^2=(a+b)(a-b)$ with $a=w^2$ and $b=4$.
This gives me $w^4-16=(w^2+4)(w^2-4)$.
But I'm not done yet, because the second factor is also a difference of squares.
I can apply the same formula again with $a=w$ and $b=2$.
This gives me $w^2-4=(w+2)(w-2)$.
So the final answer is $w^4-16=(w^2+4)(w+2)(w-2)$, and I cannot factor any further because the first factor is irreducible over the reals.