In order to factorate the trinomial, let's first find its roots using the quadratic formula:
[tex]\begin{gathered} b^2-4ac=12^2-4\cdot4\cdot9=144-144=0 \\ x_1=x_2=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-12+0}{2\cdot4}=-\frac{12}{8}=-\frac{3}{2} \end{gathered}[/tex]Now we can write the trinomial in the form:
[tex]a(x-x_1)(x-x_2)[/tex]So we have that:
[tex]4x2+12x+9=4(x+\frac{3}{2})(x+\frac{3}{2})=(2x+3)(2x+3)[/tex]So 2x + 3 is a factor of the trinomial, therefore the answer is D.
