Two planetary mass objects in the far outer Solar System --- collectively referred to here as Planet X --- have recently been hypothesized to explain the orbital distribution of distant Kuiper Belt Objects. Neither planet is thought to be exceptionally faint, but the sky locations of these putative planets are poorly constrained. Therefore, a wide area survey is needed to detect these possible planets. The Large Synoptic Survey Telescope (LSST) will carry out an unbiased, large area (around 18,000 deg$^2$), deep (limiting magnitude of individual frames of 24.5) survey (the wide-fast-deep survey) of the southern sky beginning in 2022, and is therefore an important tool to search for these hypothesized planets. Here we explore the effectiveness of LSST as a search platform for these possible planets. Assuming the current baseline cadence (which includes the wide-fast-deep survey plus additional coverage) we estimate that LSST will confidently detect or rule out the existence of Planet X in 61% of the entire sky. At orbital distances up to $sim$75 au, Planet X could simply be found in the normal nightly moving object processing; at larger distances, it will require custom data processing. We also discuss the implications of a non-detection of Planet X in LSST data.
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