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The precise meaning of the instruction in the post is UNCLEAR.
I think that the precise meaning is nonsense, if to read it literally as it is written in the post.
THEREFORE, I will do what my common sense dictates to me.
x^2(2-6x) + 4x(4-12x) = x^2(2-6x) + 8x(2-6x) = (2-6x)*(x^2+8x) = 2x*(1-3x)*(x+8). ANSWER
Solved, answered and explained.
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When you have TWO polynomials, you may talk about their greatest common factor.
When you have ONE polynomial, AS IN THIS CASE, you CAN NOT talk about the greatest common factor.
It looks like that the person, who created this " problem ", has very low care/(understanding)
on what he (or she) does write.