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

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.