What are some factors that can regulate enzyme activity?

Temperature, pH, enzyme concentration, substrate concentration, and the presence of any inhibitors or activators are just some of the factors.

Feedback inhibition ... where the product of a reaction becomes a competitive inhibitor in order to block more substrate from entering the active site.

Allosteric inhibition ... certain enzymes have regions on them away from the active site where special allosteric inhibitor proteins can bind to which change the shape and overall function of the enzyme. This is a form of noncompetitive inhibition.

Other factors could be ph, temperature, amount of substrate/enzyme ...