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 ________.

As P(x) is an odd function

Hence, $\mathrm{P}(-\mathrm{x})=-\mathrm{P}\left(\mathrm{x}\right)\Rightarrow \mathrm{P}(-3)=-\mathrm{P}\left(3\right)=-6$

Let $\mathrm{P}\left(\mathrm{x}\right)=\mathrm{Q}\left({\mathrm{x}}^2-9\right)+\mathrm{ax}+\mathrm{b}$

(where Q is quotient and (ax + b) = g(x) = remainder)

Now $\mathrm{P}\left(3\right)=3\mathrm{a}+\mathrm{b}=6$               …. (1)

        $\mathrm{P}(-3)=-3\mathrm{a}+\mathrm{b}=-6$    ….. (2)

Hence, b = 0 and a = 2

Hence, g(x) = 2x $\Rightarrow \mathrm{g}\left(2\right)=4$