The question is simply rearranging the question to solve for the term with the degree of 2.
The question states,
[tex](x^2 - 4) \div (x+2) = (x-2)[/tex]
You can multiply each side by (x + 2) to get rid of the division sign:
[tex](x^2 - 4) = (x+2) \times \boxed{(x-2)}[/tex]
The polynomial that will fill in the blank is (x - 2).