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Question

When a polynomial p(x) is divided by x1, the remainder is 3. When p(x) is divided by x3, the remainder is 5. If r(x) is the remainder when p(x) is divided by (x1)(x3), then the value of r(2) is

A
2
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B
1
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C
0
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D
4
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Solution

The correct option is B 0
Given P(1)=3
P(3)=5
Let r(x)=ax+b
So P(x)=(x1)(x3)q(x)+ax+b
P(1)=a+b a+b=3
P(3)=3a+b 3a+b=5
a=1,b=2
r(x)=ax+b=x+2
r(2)=(2)+2)
r(2)=0

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