By using identity we got the factorization form of [tex]x^8-16[/tex] as [tex](x^4+4)(x^2+2)(x-\sqrt2)(x+\sqrt2)[/tex]
factorization is a way of writing any expression in form of product of some expressions
Given polynomial
[tex]x^8-16[/tex]
We can factorize it as
[tex]x^8-16\\\\(x^4)^2-4^2\\\\(x^4+4)(x^4-4)\\\\(x^4+4)((x^2)^2-2^2)\\\\(x^4+4)(x^2+2)(x^2-2)\\\\(x^4+4)(x^2+2)(x^2-(\sqrt2)^2)\\\\(x^4+4)(x^2+2)(x-\sqrt2)(x+\sqrt2)[/tex]
By using identity we got the factorization form of [tex]x^8-16[/tex] as [tex](x^4+4)(x^2+2)(x-\sqrt2)(x+\sqrt2)[/tex]
To learn more about factorization visit :brainly.com/question/25829061
