Check whether 7 + 3x is a factor of \(3x^3 + 7x\).

Let \(p(x) = 3x^3 + 7x\)

To check, whether 7 + 3x is a factor of \(3x^3 + 7x\).
By factor theorem, \(7 + 3x = 0\)
\(\therefore x = \frac{-7}{3} \)

\(\therefore p(\frac{-7}{3} ) = 3(\frac{-7}{3} )^3 + 7(\frac{-7}{3} )\)
\(\Rightarrow p(\frac{-7}{3} ) = - 3×(\frac{343}{27} ) - \frac{49}{3} \)
\( \Rightarrow p(\frac{-7}{3} ) = \frac{-1470}{27} \)
\(\Rightarrow p(\frac{-7}{3} ) = \frac{-490}{9} \)

Hence, 7 + 3x is not the factor of \(3x^3 + 7x\) since the remainder is not zero.