Respuesta :

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
For this case we have the following polynomial:
 3x4 + 6x3 + 9x2
 We observe that the polynomial has 3x2 as a common factor.
 Therefore, by rewriting the polynomial we have:
 3x2 (x2 + 2x + 3)
 Answer:
 
The factorization for this case is given by:
 
3x2 (x2 + 2x + 3)
 
option B