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Question

Polynomial P(x) contains only terms of odd degree. When P(x) is divided by (x3), the remainder is 6. If P(x) is divided by (x29), then the remainder is g(x), then the value of g(2), is:

A
4
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B
4
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C
0
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D
2
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Solution

The correct option is A 4
As P(x) is an odd function
Hence, P(x)=P(x)P(3)=P(3)=6
Let P(x)=Q(x29)+ax+b
(where Q is quotient and (ax+b) = g(x) = remainder)
Now P(3)=3a+b=6 (1)
P(3)=3a+b=6 (2)
Solving (1) and (2) we get
b=0 and a=2
Hence, g(x)=2xg(2)=4

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