Answer
$(x^4+16)(x+1)(x-1)(x^2+1)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
Hence here: $x^8+15x^4-16=\\=x^8-x^4+16x^4-16\\=x^4(x^4-1)+16(x^4+1)\\=(x^4-1)(x^4+16)\\=(x^4+16)((x^2)^2-1^2)\\=(x^4+16)(x^2-1)(x^2+1)\\=(x^4+16)(x^2-1^2)(x^2+1)\\=(x^4+16)(x+1)(x-1)(x^2+1)$
