Question

Factor this completely

P(x)=x^4-256

Answer 1

`\bf p(x)=x^4-256\qquad \boxed{2^8=256}\qquad p(x)=x^(2\cdot 2)-2^(4\cdot 2) \\\\\\ p(x)=(x^2)^2-(2^4)^2\implies p(x)=[x^2-2^4]~[x^2+2^4] \\\\\\ p(x)=[x^2-(2^2)^2]~[x^2+2^4]\implies p(x)=[(x-2^2)(x+2^2)]~[x^2+2^4] \\\\\\ p(x)=(x-4)(x+4)(x^2+16)`