Answer
$(x-1)^2(x-2i)(x+2i)$
Work Step by Step
Try to factor P as $P(x)=x^4-x^3-x^3+x^2+4x^2-4x-4x+4=x^3(x-1)-x^2(x-1)+4x(x-1)-4(x-1)=(x-1)(x^3-x^2+4x-4)=(x-1)[x^2(x-1)+4(x-1)]=(x-1)^2(x^2+4)=(x-1)^2(x-2i)(x+2i)$
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