In real numbers:
[tex]3n^3+4n^2+24n+32=n^2(3n+4)+8(3n+4)\\\\=(3n+4)(n^2+8)[/tex]
In complex numbers:
[tex]=(3n+4)(n^2-(-8))=(3n+4)(n^2-(i\sqrt8)^2)\\\\=(3n+4)(n-i\sqrt8)(n+i\sqrt8)\\\\\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2\\\\=(3n+4)(n-2i\sqrt2)(n+2i\sqrt2)[/tex]
Used [tex](a-b)(a+b)=a^2-b^2[/tex]
