3. 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, $$7 + 3x = 0$$ i.e. x = -7/3
So, $$p(-7/3) = 3(-7/3)^3 + 7(-7/3)$$
i.e. $$p(-7/3) = - 3×(343/27) - 49/3$$
i.e.$$p(-7/3) = -1470/27$$
i.e.$$p(-7/3) = -490/9$$
Hence, 7 + 3x is not the factor of $$3x^3 + 7x$$ since the remainder is not zero.