Your answer would be C, or [tex]3x(x^{2} -4x+9)[/tex].
To factor this polynomial, take out a greatest common factor from all of the terms.
In this case, we can look at the coefficients of x and x itself separately, and then combine them at the end.
The coefficients of x are 3, -12, and 27.
The greatest common factor between these numbers would be 3, as each of those numbers are divisible by 3.
Now, looking at x, you see [tex]x^{3}, x^{2}, x[/tex].
The greatest common factor between these numbers would just be x, as all of these are divisible by x.
Now, combine these factors. 3 and x are the two greatest common factors, and putting them together, you get 3x.
To finish factoring this, factor out 3x from the polynomial, and combine them.
The polynomial is [tex]3x^{3}-12x^{2} +27x[/tex]. To factor 3x out of them, divide each term by 3x.
[tex]3x((3x^{3} / 3x) - (12x^{2} / 3x) + (27x / 3x))[/tex]
[tex]3x(x^{2} - 4x + 9)[/tex]
That would be your answer, C.
Good luck!
