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Question

What is the sum of the remainders when the polynomial p(x)=x2+3x+1 is divided by x1 and x2?

A
11
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B
5
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C
16
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D
14
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Solution

The correct option is C 16
From remainder theorem, we know
The remainder when p(x) is divided by x1, the remainder is p(1)


p(1)=12+3(1)+1=1+3+1=5

Similarly,
The remainder when p(x) is divided by x2, the remainder is p(2)

p(2)=22+3(2)+1=4+6+1=11

The sum of remainders = 5 + 11 = 16

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