Question

factor: x^6-4x^4-x^2+4

Answer 1

\[\eqalign{
x^6-4x^4-x^2+4&=(x^6-4x^4)-(x^2-4) \\
&=x^4(x^2-4)-(1)(x^2-4) \\
&=(x^4-1)(x^2-4) \\
&=((x^2)^2-1)(x^2-4) \\
&=(x^2-1)(x^2+1)(x+2)(x-2) \\
&=(x-1)(x+1)(x^2+1)(x+2)(x-2) \\
&=(x+2)(x+1)(x-1)(x-2)(x^2+1) \\

}\]