A polynomial P(x) is divisible by x-5. If P(x) is divided by x-2 then the quotient is polynomial Q(x) and the remainder is 30. What is the remainder when Q(x) is divided by x-5?
If P(x)= (x-2)Q(x)+30, and Q(x)=(x-5)R(x)+S, then P(x)= (x-2)(x-5)R(x) +(x-2)S +30. Since P(x) is divisible by (x-5), P(5)=0, so 3S+30=0, and then S=-10.
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