Kingdom(s)
An elaborate and historically informed reading of this variation (the Quarto with "kingdoms" and the Folio with "kingdom") reads:
Though this variant could easily result from an accident of transmission in either text -- addition or omission of terminal s being among the commonest of all errors - the despised Quarto reading in fact makes good sense, and in the absence of the Folio might never have been emended. Until later in the seventeenth century the noun kingdom could mean "kingly function, authority, or power" (OED, sb. 1), so that a Jacobean audience could easily have understood the Quarto phrase to mean "the division of powers." Alternatively, Gloucester might be using "kingdoms" proleptically. Lear intends to divide the united kingdom of Britain into three territories, each of which will remain "perpetual and "hereditary ever" in the possession of one daughter and her descendants: Lear is thus effectively creating three "kingdoms", in the division of which he has shown no partiality to either Albany or Cornwall. Since, in order for Kent and Gloucester to speak of them, the territorial divisions must clearly have been decided, the three "kingdoms" in some sense already exist. Moreover, to a Jacobean audience, the names of the two Dukes would have strongly suggested two British "kingdoms" with which they were thoroughly familiar. Albany, the old name for all of Britain north of the Humber, was eventually identified, more loosely, with Scotland; it was one of the three territories into which the legendary Brutus had divided the island. Cornwall was a separate kingdom until the tenth century; from the fourteenth century the Duke of Cornwall was also always the Prince of Wales, thereby uniting the two western territories under one nobleman...To an audience of 1605, for whom the reunification of "the kingdoms" was an immediate political issue, the Quarto's plural should not have caused any perplexity....There is thus no reason to deny the authority of either the Quarto's plural or the Folio's singular.
From Gary Taylor and Michael Warren's preface to (the aptly entitled) The Division of the Kingdoms: Shakespeare's Two Versions of King Lear, ed. Gary Taylor and Michael Warren (Oxford: Clarendon Press, 1983), v-vii . If you are interested in researching the textual issues at stake in Lear, you may well want to have a look at this collection. (Note: Taylor and Warren use the old spelling, but we have modernized it for the purpose of this assignment).