Polynomial `P(x)` is divided by `(x-3)` , the remainder if 6.If `P(x)` is divided by `(x^2-9)` , then the remainder is `g(x)` . Then the value of `g(2)` is ___________.

Explanation

As P(x) is an odd function
Hence, `P(-x)=-P(x)impliesP(-3)=-P(3)=-6`
Let `P(x)=Q(x^(2)-9)+ax+b`
(where Q is quotient and (ax+b)=g(x)=remainder)
Now `P(3)=3a+b=6" "(2)`
Hence, b=0 and a=2
Hence, `g(x)=2x mpliesg(2)=4`