Question 1082119

{{{-3x^2-27}}}

{{{-3(x^2+9)}}}

{{{-3(x^2+3^2)}}}........here we have the sum of squares {{{(x^2+3^2)}}} and we can write it as the difference of squares if we write {{{3^2}}} as {{{-3^2(-1)}}}, and we know that {{{-1=i^2}}}; so, we have {{{(x^2-3^2i^2)}}} or
{{{(x^2-(3i)^2)}}} now factor it as the difference of the squares and you have  {{{x^2+9=(x -3i) (x + 3i)}}}

plug it in:
{{{-3(x -3i)(x + 3i)}}}....multiply {{{-3(x -3i)}}}

{{{(-3x -(-3)3i)(x + 3i)}}}

{{{(-3x +9i)(x + 3i)}}}

answer:

D ) {{{(-3X+9i)(x+3i)}}}