Form 4 More about polynomials.

When a polynomial P(x) is divided by x+1, the remainders are -7:
=> P(-1)=-7...(1)

When a polynomial P(x) is divided by x+2, the remainders are -25:
=> P(-2)=-25...(2)

When P(x) is divided by (x+1)(x+2), let the remainder be (ax+b):
P(x)=(x+1)(x+2)Q(x)+(ax+b)...(*)

Sub (1) into (*): P(-1)=-a+b=-7...(3)
Sub (2) into (*): P(-2)=-2a+b=-25...(4)

(3)-(4): a=18 and b=11

Hence, the remainder is 18x+11

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