First we have to take out the greatest common factor from the given polynomial. If you observe the expression, you can see the greatest common factor that exist is 3x². So taking it out as common, the factorization of the polynomial will be:
[tex]3 x^{4}+6 x^{3}+9 x^{2} \\ \\
=3 x^{2} ( x^{2} +2x+3) [/tex]
So, the option B gives the correct answer to this question