Question

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 1

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.

Answer 2

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