Noncanonical poly(A) polymerases are frequently tethered to mRNA 3' untranslated regions and regulate poly(A) tail length and resulting translation. In the brain, one such poly(A) polymerase is Gld2, which is anchored to mRNA by the RNA-binding protein CPEB1 to control local translation at postsynaptic regions. Depletion of CPEB1 or Gld2 from the mouse hippocampus results in a deficit in long-term potentiation (LTP), but only depletion of CPEB1 alters animal behaviour. To test whether a related enzyme, Gld4, compensates for the lack of Gld2, we separately or simultaneously depleted both proteins from hippocampal area CA1 and again found little change in animal behaviour, but observed a deficit in LTP as well as an increase in long-term depression (LTD), two forms of protein synthesis-dependent synaptic plasticity. RNA-seq data from Gld2, Gld4, and Gld2/Gld4-depleted hippocampus show widespread changes in steady state RNA levels, alternative splicing, and alternative poly(A) site selection. Many of the RNAs subject to these alterations encode proteins that mediate synaptic function, suggesting a molecular foundation for impaired synaptic plasticity.