  Linear Temporal Logic (LTL) is a widely used specification framework for
linear time properties of systems. The standard approach for verifying such
properties is by transforming LTL formulae to suitable $\omega$-automata and
then applying model checking.
  We revisit Vardi's transformation of an LTL formula to an alternating
$\omega$-automaton and Wolper's LTL tableau method for satisfiability checking.
We observe that both constructions effectively rely on a decomposition of
formulae into linear factors.
  Linear factors have been introduced previously by Antimirov in the context of
regular expressions.
  We establish the notion of linear factors for LTL and verify essential
properties such as expansion and finiteness.
  Our results shed new insights on the connection between the construction of
alternating $\omega$-automata and semantic tableaux.
