# ag.algebraic geometry – reducibility of an element in a linear system in \$mathbb{P}^3\$

It is known that in characteristic zero, in a linear system (not necessarily complete) in $$mathbb{P}^3$$ a general element is irreducible. Now my question is the following:
Suppsoe we have a subspace $$V subset H^0(mathbb{P}^3, mathcal{O}(3))$$ of dimension $$ge 3$$. Then is it possible always to find an element in $$V$$ which is reducible ?