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# 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.