[tex]\displaystyle\\
x ^3 + 7x^2 + 16x + 12 = ?\\
~~~~~7x^2 = 3x^2+4x^2 \\
~~~~~16x=12x+4x\\\\
x ^3 + 7x^2 + 16x + 12 =\\
=x ^3 + 3x^2+4x^2 + 12x+4x + 12 =\\
=(x ^3 + 3x^2)+(4x^2 + 12x)+(4x + 12) =\\
=x^2(x + 3)+4x(x + 3)+4(x + 3) =\\
=(x+3)(x^2+4x+4)=\\
=(x^2+4x+4)(x+3)=\\
=(x^2+2\cdot x\cdot 2+2^2)(x+3)=\\
=\boxed{\bf (x+2)^2(x+3)}
[/tex]
