What is the remainder when a^3-4 is divided by a+2?

-12

Step-by-step explanation:

Use synthetic division to find the remainder:

a + 2 yields the synthetic division divisor -2.  The four coefficients of a^3 - 4 are {1, 0, 0, -4}.  Setting up synthetic division results in:

-2   /   1    0    0    -4

              -2    4     -8

         1     -2    4    -12

The remainder is -12.  This is also the value of a^3 - 4 when a = -2.