Question

Factor over the complex numbers, if possible: 12m^2 + 27

A)
3(2m + 3i)^2
B)
3(2m - 3i)^2
C)
3(2m + 3i)(2m -3i)
D)
not possible

Answer 1

first find the GCF

Answer 2

\[\begin{align*}
12m^2+27&=3(4m^2+9)\\
&=3((2m)^2-(-9))\\
&=3((2m)^2-(3i)^2)
\end{align*}\]
Now factor as a difference of squares.