Final answer:
To find the values of A and B, set up a system of equations using the given information. Solve the system of equations to find A and B.
Step-by-step explanation:
To find the values of A and B, we need to set up a system of equations using the given information. Since the remainder when the polynomial is divided by x+1 is 3, we can substitute x=-1 into the polynomial and set it equal to 3:
A(-1-1)² + B(-1+2)² = 3
Next, we can use the remainder when the polynomial is divided by x-2, which is -15, to set up another equation:
A(-2-1)² + B(-2+2)² = -15
Simplifying each equation, we get:
4A + 9B = 12
B = -15
Substituting B = -15 into the first equation, we can solve for A:
4A + 9(-15) = 12
4A - 135 = 12
4A = 147
A = 36.75
Therefore, the values of A and B are A = 36.75 and B = -15.