Final answer:
The auditor of Borax, Inc. would most likely review Borax board minutes and obtain a management representation letter to obtain assurance of all guarantees made by Borax for Ajax, Inc.'s indebtedness.
Step-by-step explanation:
The most likely approach that the auditor of Borax, Inc. would use to obtain assurance that all guarantees of Ajax, Inc.'s indebtedness by Borax have been detected is option 2) Review Borax board minutes and obtain a management representation letter.
Reviewing Borax board minutes allows the auditor to gather information on any discussions or decisions related to guaranteeing Ajax's indebtedness. Obtaining a management representation letter from Borax's management provides a written statement confirming any guarantees made by Borax.
This approach ensures that the auditor has obtained direct evidence from reliable sources to confirm the guarantees of Ajax's indebtedness by Borax.