Polynomial P(x) contains only terms of odd degree. When P(x) is divided by (x−3), the remainder is 6. If P(x) is divided by (x2−9), 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 A4 As P(x) is an odd function Hence, P(−x)=−P(x)⇒P(−3)=−P(3)=−6 Let P(x)=Q(x2−9)+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)=2x⇒g(2)=4