Fully factorise \( 3 f^{2}+7 f \)

To fully factorise the expression \( 3f^{2} + 7f \), we begin by identifying the common factors in both terms. Here, we can see that both terms have a factor of \( f \). So, we can factor out \( f \): \[ f(3f + 7) \] Now, we check if \( 3f + 7 \) can be factored further. Since \( 3f + 7 \) cannot be factored into simpler polynomial terms with integer coefficients, the factorization is complete. Thus, the fully factorized form of \( 3f^{2} + 7f \) is: \[ f(3f + 7) \]