ANSWER
[tex](v + 3)(7 {v}^{2} + 3)[/tex]
EXPLANATION
The given expression is
[tex]7 {v}^{2} (v + 3) + 3(v + 3)[/tex]
The greatest common factor is (v+3).
We factor to obtain:
[tex](v + 3)(7 {v}^{2} + 3)[/tex]
Therefore the factored form is:
[tex](v + 3)(7 {v}^{2} + 3).[/tex]