J.R. S. answered 03/28/18
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Glycolysis is the breakdown of glucose to form pyruvate. So, it is essentially a decomposition reaction, according to chemical definitions. But since it also results in synthesis of pyruvate, it might be considered a synthesis, but that would be a stretch because of the intervening steps. In general, in chemistry, synthesis is considered to be of the form A + B => C.
Decomposition is considered to be A => B+ C. So, glycolysis meets the definition of decomposition better than synthesis. It is clearly NOT pyrolysis nor double displacement.