When x³+ax²+4 is divided by x+1,   the remainder is 6 greater than the    remainder when it is divided by x-2,  the value of a is

To solve this problem, we will use the Remainder Theorem which states that the remainder of a polynomial f(x) divided by (x-a) is f(a).

1. According to the problem, when x³+ax²+4 is divided by x+1, the remainder is 6 greater than the remainder when it is divided by x-2. So, we can write this as:

   f(-1) = f(2) + 6

2. Substitute x = -1 and x = 2 into the polynomial x³+ax²+4:

   (-1)³+a(-1)²+4 = (2)³+a(2)²+4 + 6

3. Simplify both sides:

   -1+a+4 = 8+4a+4+6

4. Further simplify:

   a+3 = 18+4a

5. Rearrange the equation to solve for a:

   a - 4a = 18 - 3

6. Simplify:

   -3a = 15

7. Solve for a:

   a = -15/3 = -5

So, the value of a is -5.