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(10) 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 $\mathrm{P}\left(3\right)=3\mathrm{a}+\mathrm{b}=6 \left(1\right)$
   $\mathrm{P}(-3)=-3\mathrm{a}+\mathrm{b}=-6 \left(2\right)$
Hence, b = 0 and a = 2
Hence, $\mathrm{g}\left(\mathrm{x}\right)=2\mathrm{x}\Rightarrow \mathrm{g}\left(10\right)=20$.