In order to rewrite the given polynomial, first let's find the zeros using the quadratic formula:
[tex]\begin{gathered} x^2+6x+9=0 \\ a=1,b=6,c=9 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-6+\sqrt[]{36-36}}{2}=\frac{-6+0}{2}=-3 \\ x_2=\frac{-6-0}{2}=-3 \end{gathered}[/tex]Now, let's rewrite the polynomial in the factored form:
[tex]\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=1(x-(-3))(x-(-3)) \\ y=(x+3)(x+3) \end{gathered}[/tex]Therefore the correct option is B.
