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ziro4ka [17]
3 years ago
12

Factor the polynomial function over the complex numbers. f(x)=x^3-2x^2+3x-6

Mathematics
1 answer:
Airida [17]3 years ago
6 0

f(x)=x^3-2x^2+3x-6=x^2(x-2)+3(x-2)=(x-2)(x^2+3)\\\\i=\sqrt{-1}\to i^2=-1\\\\x^2+3=x^2-(-3)=x^2-3i^2=x^2-(\sqrt3)^2i^2)=x^2-(i\sqrt3)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\boxed{f(x)=(x-2)(x-i\sqrt3)(x+i\sqrt3)}

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