$$\\\frac{(X^4+8X^3+12x^2-2x-9)}{(x+2)}\\\\ $Let the numerator be f(x)$\\ $find f(-2)\\ (-2)^4+8(-2)3+12(-2)^2-2(-2)-9\\ =16-64+48+4-9\\ =-29\\ \ne0 \\ $so (x+2) is not a factor of the numerator$\\ $so this cannot be simplified$$$
$$\\\frac{(X^4+8X^3+12x^2-2x-9)}{(x+2)}\\\\ $Let the numerator be f(x)$\\ $find f(-2)\\ (-2)^4+8(-2)3+12(-2)^2-2(-2)-9\\ =16-64+48+4-9\\ =-29\\ \ne0 \\ $so (x+2) is not a factor of the numerator$\\ $so this cannot be simplified$$$
