Check whether 7+3x is a factor of 3x³+7x

We will find the remainder by the factor theorem.
Factor theorem: If x-a is a factor of a polynomial p(x) then p(a)=0.
Let the given polynomial be, p(x)=3x³+7x
Put, 7+3x=0 ⇒ 3x=-7 ⇒ x=-7/3
Replace x=-7/3 in p(x)=3x³+7x
p(-7/3) = 3(-7/3)³+7(-7/3) = 3(-343/27)+(-49/3) = -343/9 - 49/3 = (-343 - 147)/9 = -490/9
Since p(-7/3) ≠ 0
Hence, 7+3x is not a factor of 3x³+7x