Help!!!! with Pre-Calculus?

Question

Let f(x) = (18x^9-387x^8+3361x^7-14692x^6+17910x^5+164911x^4-852405x^3+1052928x^2+1384948x-1172528.

Determine the number of complex zeros of f(x) in the complex region (-infinity,-3) U (3, infinity). Justify your answer.

f(x)=18x^9-387x^8+3361x^7-14692x^6+17910x^5+164911x^4-852405x^3+1052928x^2+1384948x-1172528

Answer 1

Taking out x^6 f(x)= x^6( 18x^3 -387x^2 +3361x -14692)If you study the parenthesis as a function

its derivative is 54x^2 -774x +3361 has no real roots so it is always positive.
So the parenthesis increases from -infinity to + infinity.
There is only one real root,but at x=3 it is still negative

So the real root is >3 and there are two complex roots.(complex conjugates)

I really don´t understand the meaning of a "complex region(-infinity,-3)"
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