Is x+2 a factor of x^3+8?

Yes x+2 is a factor of x^3+8
Because Since both terms are perfect cubes, factor using the sum of cubes formula, a^3+b^3=(a+b)(a^2-ab+b^2) where a=x and b=2 so if you use that formula to find factors you would get (x+2)(x^2-2x+4) so x+2 is a factor of x^3+8
Hope that helps