Is x+3 a factor of x^4-2x^3-15x^2-14x-12

Use synthetic division here, if you know it.  Use -3 as divisor and use the coefficients 1  -2  -15  -14  -12.  If there is no remainder, then x+3 is a factor of the given polynomial.

     
-3  /  1   -2   -15   -14   -12
             -3     15      0    42
     
         1   -5      0    -14    30

There's a non-zero remainder:  30.  This means that the polynomial has the value 30 when x = -3, and that (x+3) is NOT a factor of the poly.