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Question

Let P(x) be a polynomial, which when divided by x−3 and x−5 leaves remainders 10 and 6 respectively. If the polynomial is divided by (x−3)(x−5) then the remainder is

A
2x+16
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B
16
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C
60
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D
2x16
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Solution

The correct option is A 2x+16
Let the remainder be, ax+b
From the given data,
P(x)=(x3)(x5)q(x)+(ax+b)

When x=3, P(3)=10
and when x=5, P(5)=6
The remainder is,
3a+b=10
5a+b=6

Solving the above equations,
a=2,b=16
Thus, the remainder is, 2x+16.

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