Why does f(x) = -2x^2(x^2 - 2) have no real zeroes?

Question

Why does f(x) = -2x^2(x^2 - 2) have no real zeroes?

 

If it were (x - 2) in parens, that would be a factor of 0 and the answer would be 2. Why can't (x^2 - 2) be a factor?

Answer 1

f(x) = -2x²(x²-2) does have three real zeros, at x=0 and x=±√2.  Click in the link below to view the graph of f(x).

 

http://www.wyzant.com/resources/files/287465/zeros_of_a_polynomial