When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B

When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B

When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.

Answer：P(1) = 15 + 2(13) +A × (1) + B = 2 : remainder theorem
P(-3) = (-3)5 + 2(-3)3 +A × (-3) + B = -314
A = 4 and B = -5 : solve the above systems of equations.